Question

An astronaut holds a rock 100m above the surface of Planet X . The rock is then thrown upward with a speed of 15m/s , as shown in the figure. The rock reaches the ground 10s after it is thrown. The atmosphere of Planet X has a negligible effect on the rock when it is in free fall.

Answer 1

Answer:
`5 m/s^(2)`

Step-by-step explanation:

The described situation is is related to vertical motion (and free fall). So, we can use the following equation that models what happens with this rock:

`y=y_(o)+V_(o)sin\theta t-(1)/(2)gt^(2)` (1)

Where:

`y=0m` is the rock's final height

`y_(o)=100 m` is the rock's initial height

`V_(o)=15 m/s` is the rock's initial velocity

`\theta=90\°` is the angle at which the rock was thrown (directly upwards)

`t=10 s` is the time

`g` is the acceleration due gravity in Planet X

Then, isolating
`g` and taking into account
`sin(90\°)=1`:

`g=(-(2)/(t^(2)))(y-y_(o)-V_(o)t)` (2)

`g=(-(2)/((10 s)^(2)))(0 m-100 m-(15 m/s)(10 s))` (3)

Finally:

`g=5 m/s^(2)` (4) This is the acceleration due gravity in Planet X