Question

(a)

Calculate the height (in m) of a cliff if it takes 2.37 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.19 m/s. (Enter a number.)
(b)
How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.)

Answer 1

(a) Let the base of the cliff be the origin, so that the rock's height y at time t is

y = h + (8.19 m/s) t - 1/2 gt²

where h is the height of the cliff. The rock hits the ground when y = 0. Solve for h when t = 2.37 s :

0 = h + (8.19 m/s) (2.37 s) - 1/2 (9.80 m/s²) (2.37 s)²

⇒ h ≈ 8.11 m

(b) If the rock is thrown straight down with the same speed, its height at time t would be

y = 8.11 m - (8.19 m/s) t - 1/2 gt²

Solve for t when y = 0 (use the quadratic formula and ignore the negative solution) :

t ≈ 0.699 s