Question

A ball is thrown in the air from a ledge. Its height in feet is represented by f16(2-5x - 6), where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground. How many şeconds does it take the ball to reach the ground?

Answer 1

Height in feet is represented by $f(x) = -16(x^2-5x-6)$

The height of the ball is 0 feet when it hits the ground.

So we replace height f(x) by 0 and solve for x  to find the time taken to reach the ground

$f(x) = -16(x^2-5x-6)$

$0= -16(x^2-5x-6)$ ( divide by -16 on both sides)

$0=(x^2-5x-6)$

Now factor it

(x-6)(x+1) =0

x-6 =0  and x+1=0

x=6 and x=-1

Time cannot be negative so we ignore -1

x = 6 seconds

It will take 6 seconds for the ball to reach the ground.