Question

Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth.

(a) At what velocity must the supplies be launched?
(b) What is unreasonable about this velocity?
(c) Is there a problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height?
(d) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.

The velocity at which the supplies must be launched is approximately:

a) 9,800 m/s
b) 11,200 m/s
c) 13,400 m/s
d) 15,600 m/s

Answer 1

The supplies must be launched with an initial velocity of approximately 11,200 m/s, which exceeds the escape velocity of the Earth. There is no problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height. The premise of launching supplies straight up to reach astronauts in orbit is unreasonable.

Step-by-step explanation:

To launch supplies to astronauts in an orbit 36,000 km above the surface of the Earth, the supplies must be launched with an initial velocity of approximately 11,200 m/s. This velocity is unreasonable because it is greater than the escape velocity of the Earth, which is around 11,186 m/s. This means that the supplies would have enough velocity to escape Earth's gravitational pull and move away from Earth.

There is no problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height. Since they are both in the same orbit, their relative velocity will remain constant.

The premise of launching supplies straight up to reach astronauts in orbit is unreasonable. The available equation for calculating the velocity at which the supplies must be launched is applicable, but it leads to an unreasonable result because it exceeds the escape velocity.