Question

Selena is standing on a rock cliff that is 52 feet high. She tosses a pebble upward over the edge, where it hits the top of a 12 foot high boulder. The quadratic equation that models the path of the pebble is given below. How long did it take for the pebble to hit the top of the boulder? p(t)=-16t^2+12t+52​

Answer 1

The answer is t=3/8

Answer 2

Answer: At
`t=(3)/(8)`, the pebble hit the top of the boulder.

Explanation:

Since we have given that

Distance at which Selena is standing on a rock cliff = 52 feet

Height of boulder above a rock cliff = 12 foot

So, the given quadratic equation would be

`p(t)=-16t^2+12t+52`

First we derivative it w.r.t t,

`p'(t)=-32t+12`

Now, we will find the critical value,

`-32t+12=0\\\\-32t=-12\\\\t=(12)/(32)=(6)/(16)=(3)/(8)`

Now, we will check whether it is maximum or not.

`p''(t)=-32<0`

So, we get that it is maximum.

Hence, at
`t=(3)/(8)`, the pebble hit the top of the boulder.