Question

Question #23db9

Answer 1

`7.70` [m/s]

Explanation:

Taking the astronaut position as the referential origin, the ball trajectory is given by

`p(t) = (v_x t, v_y t -1/2 g_m t^2)`

where `g_m` is the free fall acceleration at the moon.

The velocity at time `t` is given by

`v(t) = d/(dt)p(t) = (v_x, v_y-g_m t)`

after `t = 9`[s] we have

`v(9) = (4,8-1.62 cdot 9) = (4,-6.58)` and the speed

`norm(v(9)) = sqrt(4^2+6.58^2) = 7.70` [m/s]