To find the vertical drop, you can use the kinematic equation for vertical motion:
d = 1/2gt^2
Where:
- d is the vertical distance dropped,
- g is the acceleration due to gravity (approximately (9.8m/s^2\)),
- t is the time taken to fall.
First, let's find the time taken to fall using the horizontal motion:
v = d/t
Given that v = 6.89m/s and d = 23.5m, we can rearrange the equation to solve for t:
t = d/v
t = 23.5m/6.89m/s
t ≈ 3.41s
Now, plug t into the equation for vertical motion:
d = 1/2 times 9.8m/s^2 times (3.41s)^2
d ≈ 1/2times 9.8m/s^2 times 11.6281s^2
d ≈ 56.9854m
So, the boulder dropped approximately 56.99m.
