Gravity formula

Question

A rock is thrown upward with a velocity of 25meters per second from the top of a 21 meter high cliff, and it misses the cliff on the way back down. When will the rock be 11 meters from the water, below? Round your answer to two decimal places.

Answer 1

The height formula is:

 

h(t) = -(1/2)gt² + v₀t + h₀

• h(t) height of the object at time t
• g = acceleration due to gravity = 9.8 m/s²
• t = time in seconds
• v₀ = initial velocity of the object (+ is up, m- is down) = 25 m/s
• h₀ = initial height = 21 m

 

h(t) = -(1/2)gt² + v0t + h0

h(t) = -4.9t² + 25t + 21

 

We want h(t) = 11 m

 

11 = -4.9t² + 25t + 21

0 = -4.9t² + 25t + 10

 

Use the quadratic formula to solve for t.  You'll get two values for t, one positive and one negative.  Since we can't go back in time, the positive value is the answer.