Calculus question

Question

Please help A stone was dropped off a cliff and hit the ground with a speed of 80 ft/s. What is the height of the cliff? (Use 32 ft/s² for the acceleration due to gravity.)

Answer 1

h(t) = -16t² + h₀

v(t) = dh/dt = -32t

At the bottom, v = -80 ft/s ⇒

-32t = -80

t = -80/-32 = 2.5 sec

Plug this result for t into h(t)=0 and solve for h₀.

-16t² + h₀ = 0

-16(2.5)² + h₀ = 0

h₀ = 100 ft