A rocket is launched from the origin with an acceleration of 20.0 m/s2 in a straight line at an angle of 30.0 degrees above the horizontal. The launch acceleration lasts for 2.00 seconds at which time the fuel is exhausted. The rocket then falls with an acceleration of 9.80 m/s2 downward. What is the time it takes to reach maximum height?
Answer:
4.04 seconds
Explanation:
Context before solving:In order to solve this problem, we must keep in mind that the initial 2.00 seconds at which the fuel is exhausted does not signal when the rocket reaches its maximum height.
From this moment on, the rocket has a downward acceleration of 9.8 m/s² but it still has an upwards velocity, which we will calculate. This upwards velocity keeps the rocket moving up for a certain period of time, which we will also calculate.
For this problem, let's set the upwards direction to be positive and the downwards direction to be negative.
To find the time that the rocket takes to reach its maximum height, we are going to use the initial 2.00 seconds and find the additional seconds it takes to reach a final vertical velocity of 0 m/s. This represents the time at which the rocket stops moving and heads in the downwards direction, which takes place after the rocket has reached its maximum height.
Solving for initial velocity:The time in the air of an object in projectile motion can be found using this equation, derived from one of the constant acceleration kinematic equations.
Time in the air (projectile motion):
[tex]$t=\frac{2v_isin\theta}{g}[/tex] where g = gravitation acceleration = 9.8 m/s²Solve for [tex]v_i[/tex] by plugging in 2.00 seconds for t, 30 degrees for theta, and 20.0 m/s² for acceleration, since this is not a constant acceleration problem.
[tex]$2.00=\frac{2v_isin(30)}{20.0}[/tex]Multiply sin(30) and 2 together.
[tex]$2=\frac{v_i}{20}[/tex]Multiply 20 to both sides of the equation.
[tex]$40=v_i[/tex] [tex]v_i=40[/tex]Finding the vertical component:Now we know that the initial velocity of the rocket is 40 m/s. We need to solve for the vertical component of the rocket's velocity in order to solve for the additional time it took after the 2.00 seconds to reach its maximum height.
Vertical component:
[tex](v_i)_y=v_i \times sin\theta[/tex] [tex](v_i)_y=(40) \times sin(30)[/tex][tex](v_i)_y=20[/tex]The vertical component of the velocity vector is 20 m/s.
Finding additional seconds after 2.00 s:Now, in order to solve for the additional seconds that the rocket took to reach its maximum height, let's use one of the kinematic constant acceleration equations that uses the variables [tex]v_f[/tex], [tex]v_i[/tex], [tex]a[/tex], and [tex]t[/tex].
[tex]v_f=v_i + at[/tex]Since we are trying to solve for time, we need to use this equation in terms of the vertical direction, aka the y-direction. Time is the same in either case.
[tex](v_f)_y=(v_i)_y+a_yt[/tex]The final vertical velocity of this rocket is 0 m/s at the top, or its maximum height. We found that the vertical component, aka the rocket's initial vertical velocity, is 20 m/s. The acceleration is given to us: -9.8 m/s² (since it's falling downwards, the acceleration must be negative because we already established this in the beginning).
We are trying to solve for time t. Substitute the known values into the equation.
[tex]0=(20)+(-9.8)t[/tex]Subtract 20 from both sides of the equation.
[tex]-20=-9.8t[/tex]Divide both sides of the equation by -9.8.
[tex]2.040816327=t[/tex] [tex]t=2.04\ \text{seconds}[/tex] Finding total time to reach max height:Now we can take this time and add it to the initial 2.00 seconds of the rocket. This time we just solved for is the time after these initial seconds that the rocket kept going upwards, since its initial vertical velocity was not 0 m/s yet.
[tex]2.00+2.04=4.04 \ \text{seconds}[/tex]The time that the rocket takes to reach its maximum height is 4.04 seconds.
Answer:
4.04 second is your answer hope it help you........
A catapult with a spring constant of 10,000 N/m is used to launch a target from the deck of a ship. The spring is compressed a distance of 0.5 m
before the 1.56-kg target launched. What is the target's velocity as it leaves the spring?
Please help.
(A) 10m/s
(B) 20m/s
(C) 40m/s
(D) 30m/s
Answer:
(C) 40m/s
Explanation:
Given;
spring constant of the catapult, k = 10,000 N/m
compression of the spring, x = 0.5 m
mass of the launched object, m = 1.56 kg
Apply the principle of conservation of energy;
Elastic potential energy of the catapult = kinetic energy of the target launched.
¹/₂kx² = ¹/₂mv²
where;
v is the target's velocity as it leaves the catapult
kx² = mv²
v² = kx² / m
v² = (10000 x 0.5²) / (1.56)
v² = 1602.56
v = √1602.56
v = 40.03 m/s
v ≅ 40 m/s
Therefore, the target's velocity as it leaves the spring is 40 m/s
A dog chases a skateboarder travelling at 10.4m/s.The skateboarder speeds up with a constant acceleration for 39m over 3.3s. We want to find the acceleration of the skateboarder over the 3.3s time interval.
Answer:
The acceleration of the skateboarder over the 3.3s time interval is 3.15 m/s²
Explanation:
Acceleration can be described as the rate of change of velocity (as seen in the question). The formula to be used here to determine the acceleration is
Acceleration (in m/s²) = velocity (m/s) ÷ time (s)
Acceleration = 10.4 ÷ 3.3
Acceleration = 3.15 m/s²
Thus, the acceleration of the skateboarder over the 3.3s time interval is 3.15 m/s²
A man carries a load of mass 2.6kg from one end of a uniform pole 100cm long which has a mass 0.4kg. The pole rest on his shoulder at a point 60.0cm from the load and he holds it by the other end. What vertical force must be applied by his hand and what is the force on his shoulder?
Answer:
F = 39.2 N (hand force) and N = 68.6 N (shoulder force)
Explanation:
In this exercise we must use the rotational and translational equilibrium conditions, we have several forces: the weight (W) of the pole applied at its geometric center, the load (w1) at one end, the shoulder support (N) 60 cm from the load and hand force (F) at the other end of the pole
Let's set the reference system at the fit point of the shoulder
∑ τ = 0
We will assume that the counterclockwise turns are positive
w₁ 0.60 + W 0.1 + F₁ 0 - F 0.4 = 0
all distances are measured from the support of the man (x₀ = 0.60 m)
F = (w₁ 0.60 + W 0.1) / 0.4
F = (m₁ 0.6 + m 0.1) g / 0.4
let's calculate
F = (2.6 0.6 + 0.4 0.1) 9.8 / 0.4
F = 39.2 N
this is the force that the hand must exert to keep the system in balance
We apply the translational equilibrium condition
-w₁ -W + N - F = 0
N = w₁ + W + F
N = (m₁ + m) g + F
let's calculate
N = (2.6 + 0.4) 9.8 + 39.2
N = 68.6 N
a man climbs a ladder.which quamtities can be used to calculatethe useful power of the man
Explanation:
Power is the rate at which work is done. It is expressed as:
Power = [tex]\frac{work done}{time taken}[/tex]
To find the power of the man climbing the ladder, we must know the work he is doing and the duration of the work done.
Work done = force x distance
Since he climbs,
Force = weight = mg (mass x acceleration due to gravity)
distance = height = h
Power = [tex]\frac{mgh}{t}[/tex]
t is the time
If we know these parameters, we can find the power.
Which of the following is NOT a way that a machine makes work easier to do?
A. Change the size of a force
B. Change the type of force
C. Change the direction of the force
D. Change distance a force acts
Answer:
c
Explanation:
ur changing the way it move not to make it easier
The direction of the force, has nothing to do with how the machine will work easier. The correct option is C
A machine is any devices that make work easier. An ideal machine takes in small effort to overcome large load.
Since work has to be done in a machine, and work is the product of force and perpendicular distance, for a machine to work easier, the work done will depend on size of the force applied, the type of force applied, and also, the magnitude of the distance involved.
The direction of the force, has nothing to do with how the machine will work easier. Therefore, the correct option is C
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Which of the following is not a true statement about atomic bonds?
Answer:
Havent seen this one before but the explanation should help you out :)
Explanation:
There are only three atomic bonds.
Ionic bonding.
Covalent bonding.
Metallic bonding.
who songs are better jason derulo or Dababy , roddy ricch
Answer:
roddy i guess?
Explanation:
Answer:
Dababy and Roddy Ricch. Jason's songs use to be fire years back but now....not so much.
Explanation:
Why does a liquid thermometer work
A fossil mammoth bone was found to contain 6.25% carbon-14 percent isotope and 93.75% nitrogen-14 daughter isotope. If the half-life of carbon-14 is 5700 years old, how old is the mammoth bone?
Answer:
The mammoth bone is 22726 years old.
Explanation:
We can find how hold is the mammoth bone using the decay equation:
[tex]N(t) = N_{0}*e^{-\lambda t}[/tex] (1)
Where:
N(t): is the quantity at time t = 6.25%N₀
N₀: is the initial quantity
λ: is the decay constant
First, we need to find λ:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{5700 y} = 1.22 \cdot 10^{-4} y [/tex]
Now, by solving equation (1) for t we have:
[tex]t = \frac{ln(\frac{N(t)}{N_{0}})}{-\lambda} = \frac{ln(0.0625)}{-1.22 \cdot 10^{-4}} = 22726 y[/tex]
Therefore, the mammoth bone is 22726 years old.
I hope it helps you!
A linebacker strikes a fullback with full force in a football game.The reaction force to the force of the linebacker striking the fullback is ____.
a. the fullback falls backwards to the ground
b. the force of the fullback colliding with the ground
c. the fullback fumbles
d. the fullback applies a force to the linebacker
e. the linebacker applies a force to himself.
f. the fullback applies a force to himself
g. the sound of the pads colliding
h. there is a 3-yard loss and the linebacker is applauded
can u plz help
Define: Medium
Answer:
Medium: something in a middle position, maybe in between sizes big or small, or in a situation it's not negative or positive it's just neutral. (I'm sorry if that wasn't helpful)
Explanation:
Which statement is correct about two objects that have gravitational force?
They have mass.
They move slowly.
They are round in shape.
They have high temperature.
Answer:
1 and 2
Explanation:
The formula itself has nothing to do with shape or temperature. The formula does have mass and the speed depends on the how great the mass/radius is.
A satellite of mass 1000kg is in a circular orbit around a planet. The centripetal acceleration of the satellite in its orbit is 5m/s^2. What is the gravitational force exerted on the satellite by the planet?
A. 0N
B. 200N
C. 5000N
D. 10000N
Answer: 5000N
Explanation:
The basic principle of a circular orbit is that Fg = m × ac, so as we have the mass and the centripetal acceleration (also called normal acceleration) we just have to operate. Fg = 1000kg × 5m/s² = 5000N
The gravitational force exerted on the satellite of mass 1000 kg moving in a circular orbit with a centripetal acceleration of 5 m/s² by the planet is 5000 N (option C).
The gravitational force exerted on the satellite by the planet will be equal to the planet's gravity, which is equal to the centripetal force, so:
[tex] F_{g} = F_{c} = ma_{c} [/tex]
Where:
m: is the mass of the satellite = 1000 kg
[tex]a_{c}[/tex]: is the centripetal acceleration = 5 m/s²
The, the force acting on the satellite is:
[tex] F_{c} = ma_{c} = 1000 kg*5 m/s^{2} = 5000 N [/tex]
Therefore, the gravitational force exerted on the satellite by the planet is 5000 N (option C).
Learn more here:
https://brainly.com/question/11332442?referrer=searchResultshttps://brainly.com/question/24783651?referrer=searchResultsI hope it helps you!
If the velocity of an object is zero, then that object cannot be accelerating. | True or False
Answer: False
Explanation:
Two bodies made of the same material have same external dimension and appearance, but one is compact solid and other is hollow. When they heated for the same temperature range, is the overall volume expansion the same or different? Explain.
Answer:
Different
Explanation:
The hollow one will expand even more making it have a larger volume then the solid one so they are different
diffrence uniform and non uniform
HELP NEEDED ASAP I'M GIVING BRAINLIEST
1) Select the best answer from the choices below. Light has many properties of waves, but sometimes it also behaves like:
a
A photon
b
Polarized light
c
Ultraviolet rays
d
A stream of particles
2) What type of waves transmit signals in satellite communication?
a
Microwaves
b
X-rays
c
Gamma Rays
d
Radio Waves
3) Cell phones use digital signals to send and receive information. These digital signals travel as what kind of wave?
a
Gamma rays
b
X-rays
c
Microwaves
d
Radio waves
Answer:
1.
d . A stream of particles
2. D. Radiowave
3. Microwaves
Answer:
1.
d . A stream of particles
2. D. Radiowave
3. Microwaves
Explanation:
The Moon has a radius of 1.7 × 106 m and a mass of 7.3 × 1022 kg. Find the gravitational field on the surface of the Moon.
Answer:
10.7*[tex]10^{6}[/tex]
Explanation:
ALWAYS use significant figure rules. Remember that these rules apply to all numbers that are measurements.
In working this problem, assume the value of "g" to be 9.8 m/s2 with two (2) significant digits unless otherwise stated.
Given that a lever has a mechanical advantage of 6.0 and is 100% efficient, if the resistance is to be lifted 2.0 inches, then how far must the effort move?
De = _____ in.
12
8.0
4.0
3.0
NEXT
The effort must move 8•0
a librarian pushes a 35kg box of books across the library floor. if the carpet resists with a friction force of 91N, what force must be applied by the librarian to accelerate the box at a rate of 0.50m/s
Answer:
F = 108.5 [N]
Explanation:
To solve this type of problem we must use Newton's second law, which tells us that the sum of forces must be equal to the product of mass by acceleration.
ΣF = m*a
where:
ΣF = sum of forces [N]
m = mass = 35 [kg]
a = acceleration = 0.5 [m/s²]
f = friction force [N]
F - f = m*a
F - 91 = (35*.5)
F = 91 + 17.5
F = 108.5 [N]
A cannon sitting on the edge of a cliff 500 meters above the ground shoots a cannon ball with a horizontal velocity of 100m/s. At some point the cannon hits the ground. How far away from the point it was launched will the cannon ball land?
Answer:
1010 m
Explanation:
The following data were obtained from the question:
Height (h) of cliff = 500 m
Horizontal velocity (u) = 100 m/s
Horizontal distance (s) =?
Next we shall determine the time taken for the cannon ball to hit the ground. This can be obtained as follow:
Height (h) of cliff = 500 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) =?
h = ½gt²
500 = ½ × 9.8 × t²
500 = 4.9 × t²
Divide both side by 4.9
t² = 500/4.9
Take the square root of both side
t = √(500/4.9)
t = 10.1 s
Finally, we shall determine the horizontal distance travelled by the cannon ball.
This can be obtained by using the following formula (s = ut) as illustrated below:
Horizontal velocity (u) = 100 m/s
Time (t) = 10.1 s
Horizontal distance (s) =?
s = ut
s = 100 × 10.1
s = 1010 m
Thus, the cannon ball was launched 1010 m away from the cliff.
based on your reading "take a closer look" what can you say about the image that forms on the retina of your eye?
Answer:
it is an upside-down image but the brain realizes it and corrects it in its orientation so we see it in right direction.
Answer:
The lens of the eye is a convex lens. The image that it forms on the retina is upside down.
Explanation:
The eye makes an image, but it is upside down, the brain corrects the image and turns it right side up
An object O is acted upon by a 6 N force and a 5 N force. The angle between these two forces is 60°. Draw a scale diagram showing the forces acting on object O and determine the resultant force.
Answer:
Resultant force = [tex]\sqrt{91}[/tex]N
Explanation:
Rf = [tex]\sqrt{f1²+f2²+2.f1.f2.cos60}[/tex]
Rf = [tex]\sqrt{6²+5²+2.6.5.1/2}[/tex]
Rf = [tex]\sqrt{36+25+30}[/tex]
Rf = [tex]\sqrt{91}[/tex]
doesn't look right though...
The magnitude of resultant force is 9.54 N and it is acting an angle 33° with the direction of 5 N force.
What is force?An object's push or pull is seen as exerting a force. The interaction of the objects produces push and pull. You can also use words like stretch and squeeze to describe force.
The definition of force in physics is: The push or pull on a mass-containing item changes its velocity.
Given parameters:
Two forces are 6 N and 5N.
Angle between them is 60 degree.
So, magnitude of resultant force be = √(6² + 5² + 2× 6 × 5 × cos60°) N = = 9.54 N.
Angle of the resultant force with respect to 5 N is = tan⁻¹{6sin60°/(5 +6 cos60°) } = 33⁰.
Hence, magnitude of resultant force is 9.54 N and it is acting an angle 33° with the direction of 5 N force.
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shelly srarts from rest on her bicycle at the top of hill.after 6.0s she has reached final veocity of 14m/s. what is shelly's acceleration
A ball thrown vertically upward is caught by the thrower after 2.93 s. Find the initial velocity of the ball. The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.
Answer:
The initial velocity of the ball is 28.714 m/s
Explanation:
Given;
time of flight of the ball, t = 2.93 s
acceleration due to gravity, g = 9.8 m/s²
initial velocity of the ball, u = ?
The initial velocity of the ball is given by;
v = u + (-g)t
where;
v is the final speed of the ball at the given time, = 0
g is negative because of upward motion
0 = u -gt
u = gt
u = (9.8 x 2.93)
u = 28.714 m/s
Therefore, the initial velocity of the ball is 28.714 m/s
Which statements describe science? Check all that apply. It lacks a formal process. It involves observation. It involves experimentation. It is not updated often. It is supported by evidence
Answer:
It involves observation
It involves experimentation
It is supported by evidence
Explanation:
Science can be described as a system of knowledge based on the understanding of the natural world. The subject of science requires the scientific method - a chronological series of steps that have to be followed while trying to understand events in the natural world. These steps are:
observationformulation of hypothesistesting of the hypothesis by experimentationconclusion based on available evidence from the experimentHence, science involves observation, experimentation, and it is supported by evidence.
Answer:b. c. e
Explanation:
Why work and energy both have same unit? Give reasons?
Answer:
Explanation:
both have same unit because energy is defined as the ability to do work and work is the measure of transfer of energy when an objects moved from one place to another place so both are same thats why both have same units
A 10 V fan with a current of 2 A is turned on for 30 seconds. Calculate the energy transferred in joules,
Answer:
E = 600 J
Explanation:
Given that,
Voltage, V = 10 V
Current, I = 2 A
Time, t = 30 s
We need to find the energy transferred. Energy transferred is calculated as follows :
[tex]E=I^2Rt[/tex]
Ohm's law, V = IR, R = V/I
[tex]E=I^2\times \dfrac{V}{I}\times t\\\\E=IVt\\\\E=2\times 10\times 30\\\\E=600\ J[/tex]
So, 600 J of energy is transferred.
Answer:600J
Explanation:
Which statements accurately describe matter