Question

1. Engineers are designing a rocket to be used in deep space. If the rocket is fired from rest in deep space, the total mass of the rocket, payload, and unspent fuel must reach a speed of 1.10 ✕ 10⁴ m/s in order to accomplish other maneuvers. Due to the amount of fuel which is still onboard, the rocket, payload, and unspent fuel will have a final mass of 4.10 ✕ 10³ kg. If the design of the rocket is such that the exhaust speed is 2.55 ✕ 10³ m/s, determine the amount of fuel required to perform this maneuver.

2. A 51.0 kg astronaut has been spacewalking outside her spacecraft and realizes that she is stranded (stationary) a distance of d = 15.0 m from the outside of the spacecraft. In order to get back, she throws a 1.25 kg hammer directly away from the ship. If the spacecraft is a sphere with a 2.00 m radius, determine the distance of the hammer from the outside of the ship when she reaches the safety of the ship.

3. An ice skater with a mass of 51.0 kg is gliding across a smooth lake with a speed of 2.05 m/s when she hits a spot of ice covered with snow. After a time of 7.65 s she has slowed to a stop. Using your knowledge of momentum, determine the magnitude of the average force of friction acting on the ice skater while she slows to a stop.

Answer 1

Question 1

Initially the rockect is at rest

so initial momentum is Zero

Consider conservation of Momentum

Note: Negative sign since exhaust gas is in opposite direction

Only Unknown is amount of fuel requred to perform the maneuver

ANSWER:

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Question 2

When the astronaut throws the hammer away from the ship ,she moves towards the ship due to conservation of momentum

-------------------(a)

The astronaut takes time t to cover distance ,d =15m with velocity v_a

--------(1)

The hammer in time t ,have travelled a distance x with velocity v_h

-------------(2)

From(1) and (2)

From(a)

----------

This is the distance travelled by hammer

Distance of the hammer from the outside of the ship when she reaches the safety of the ship=x+15

ANSWER: 627m

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Question 3

Use formula

final velocity is zero

initial velocity is 2.05m/s

ANSWER:

-ve sign means force is acting against motion

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