Question

A person standing on a second floor balcony drops keys to a friend standing below the balcony. The keys are dropped from a height of 10 feet. The height in feet of the keys as they fall is given by the functionh(t)=−16t2+10, where t is the time in seconds since the keys were dropped.

The friend catches the keys at a height of 4 feet. Find the elapsed time before the keys are caught.

Answer 1

sqrt(3/8) = t

.61237 = t

Explanation:

h(t)=−16t^2+10

Let h(t) = 4

4 =−16t^2+10

Subtract 10 from each side

4-10 =−16t^2+10-10

-6 = -16 t^2

Divide by -16

-6/-16 = t^2

3/8 = t^2

Take the square root of each side

sqrt(3/8) = sqrt(t^2)

sqrt(3/8) = t

.61237 = t

We only take the positive since time is not negative