Question

I NEED HELP OF THIS! Brian "bicycle kicked" a soccer ball up from a height of 4ft off the ground with an initial upward velocity of 34 feet/sec. As the ball was coming down, Mike jumped up and at 8 ft off the ground, headed it into the goal and win the game. How long did it take for the ball to come down and reach Mike's head? Use the formula h = -16t^2 +vt + s PLEASE!

Answer 1

2 seconds

Explanation:

The formula h = -16t^2 +vt +s gives the vertical height (in feet) at time t (in seconds) for an object with an initial vertical velocity (in ft/s) of v and an initial height (in ft) of s. The problem statement tells us the ball's initial velocity is v=34 and the initial height is s=4.

Then the equation is ...

h = -16t^2 +34t +4

We want to find the value of t when h=8. There will be two solutions, one when the ball is going up, and the other when the ball is coming down. We are interested in the second solution.

8 = -16t^2 +34t +4

16t^2 -34t +4 = 0 . . . . . subtract the right side of the equation to put it into standard form

(16t -2)(t -2) = 0 . . . . . . factor the equation

Solutions are values of t that make the factors zero:

t = 2/16 or t = 2

It takes 2 seconds for the ball to come down to meet Mike's head.