Question

A swimming area in a rotating space habitat is located in a region of 1/4 g. If a diver can jump 1 m high in a 1-g region, how high can the same diver jump in the swimming area

Answer 1

The diver can jump a height of 4m in the swimming area.

Step-by-step explanation:

Using the kinematics equation of the final velocity in terms of the distance, we have that:

`v_(fy)^(2) =v_(oy)^(2)-2gy`

Since the final velocity is zero (because the diver comes to a stop in his maximum height), we conclude:

`v_(oy1)^(2) =2g_1y_1;v_(oy2)^(2) =2g_2y_2`

If we assume that the initial velocity is conserved (as the diver jumps with this initial velocity every time), we obtain:

`v_(oy1)^(2)=v_(oy2)^(2)\\\\2g_1y_1=2g_2y_2\\\\y_2=(g_1y_1)/((1)/(4) g_1) \\\\y_2=4y_1\\\\\implies y_2=4m`

In words, the diver can jump a height of 4m in the swimming area.