Hard physics question (1 Viewer)

[mr_tizzle]

Hi, i need help solving the following question, and if possible a brief explanation as to how to solve it.

Imagine that you are helping NASA plan a manned expedition to an asteroid. The asteroid has a radius of 20km, and a surface gravity of 0.011 m s-2.
NASA are concerned that the gravity on this asteroid is so small that if an astronaut inadvertently jumps, it would take too long for them to float back down again. They have asked you to estimate how much time it would take a jumping astronaut to return to the surface.

You asked some astronauts to see how high they could jump in their space suits, here on Earth. It turns out that they could raise their centres of mass by 0.21 m.
If they did a similarly powerful jump on the asteroid, how long would it take them to come back down? Type your answer, in seconds to at least one decimal place, in the box below. Do not type units.

You may assume that the gravity on the surface of the Earth is 9.8 ms-2, and that the height of their jump on the asteroid is much less than the radius of the asteroid.

 

[InteGrand]

Hi, i need help solving the following question, and if possible a brief explanation as to how to solve it.

Imagine that you are helping NASA plan a manned expedition to an asteroid. The asteroid has a radius of 20km, and a surface gravity of 0.011 m s-2.
NASA are concerned that the gravity on this asteroid is so small that if an astronaut inadvertently jumps, it would take too long for them to float back down again. They have asked you to estimate how much time it would take a jumping astronaut to return to the surface.

You asked some astronauts to see how high they could jump in their space suits, here on Earth. It turns out that they could raise their centres of mass by 0.21 m.
If they did a similarly powerful jump on the asteroid, how long would it take them to come back down? Type your answer, in seconds to at least one decimal place, in the box below. Do not type units.

You may assume that the gravity on the surface of the Earth is 9.8 ms-2, and that the height of their jump on the asteroid is much less than the radius of the asteroid.

The astronauts push off from the ground with an initial speed u, which depends on things like the strength of their legs (basically the force with which they push off the ground). We'll assume this is independent of the what planet/asteroid they are on. We need to find the value of u.

On earth, the equation of motion for their height above the ground as a function of time is , and the equation for their vertical speed as a function of time is (g is the acceleration due to gravity on earth, and t is the time since they jumped, and the equations are valid for t = 0 to the time when they land back on the ground).

They reach their max. height when speed is 0 (i.e. you stop when you reach your max. height of a jump). Speed is 0 when . Since they reach a max. height of 0.21 m, at this time, y = 0.21, so .

Solving for u gives .

Now, the equation of motion for the astronauts when they jump on the asteroid is , where a is the acceleration of gravity on the asteroid (given to us to be 0.011 m s^-2) and u was just found.

The time taken for them to fall back to the asteroid when they jump is then found by setting y_ast. to 0: . This is easily solved to give . Substituting in , with g = 9.8, and a = 0.011 m s^-2 gives t = 368.9 s, to 1 decimal place. This is about 6 minutes – annoyingly long to return from a jump.