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LUCKY_DIMON [66]
3 years ago
14

During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be lau

nched from rest from the earth's surface and is to reach a maximum height of 940 m above the earth's surface. The rocket's engines give the rocket an upward acceleration of 16.0 m/s2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance.
What must be the value of T in order for the rocket to reach the required altitude?
Express your answer to three significant figures and include the appropriate units.
Physics
1 answer:
Viktor [21]3 years ago
5 0

Answer:

6.75 seconds

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration = 16 m/s²

g = Acceleration due to gravity = 9.81 m/s²

Let y be the distance the rocket is accelerating

960-y is the distance traveled in free fall

v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 16\times y+0^2}\\\Rightarrow v^2=32y\ m/s

In free fall

v^2-u^2=2g(960-y)\\\Rightarrow 0-32y=2g(960-y)\\\Rightarrow -32y=2\times -9.81(960-y)\\\Rightarrow 960-y=\dfrac{-32}{2\times -9.81}y\\\Rightarrow 960-y=1.63098878695y\\\Rightarrow 960=2.63098878695y\\\Rightarrow y=\dfrac{960}{2.63098878695}\\\Rightarrow y=364.881828749\ m

The distance the rocket will keep accelerating is 364.881828749 m

After which it will travel 960-364.881828749 = 595.118171251 m in free fall

s=ut+\frac{1}{2}at^2\\\Rightarrow 364.881828749=0t+\frac{1}{2}\times 16\times t^2\\\Rightarrow t=\sqrt{\frac{364.881828749\times 2}{16}}\\\Rightarrow t=6.75353452598\ s

The time the rocket is accelerating is 6.75 seconds

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Explanation:

We can answer this question by applying Newton's third law of motion, which states that:

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In this problem, we can identify the Sun as object A and the Earth as object B. This means that the force of gravity exerted by the Sun on the Earth is the action, while the force of gravity exerted by the Earth on the Sun is the reaction: according to Newton's third law, these two forces are equal and opposite.

Therefore, the two forces of gravity are equal in magnitude, which is given by:

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Learn more about Newton's third law:

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Explanation:

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