Algebra 2 : Quadratic story problems

Question

A ball, thrown by a lacrosse player, is modeled by the equation h(t)=-16t^2+70t+7 where h is the height of the ball( feet) t seconds after it has left the stick. Another player catches the ball when it is 2 feet off the ground.

How long was it in the air? in seconds.

Answer 1

Hi, Drew,

The equation describes an inverted parabola. The ball rises at a rate of 70 feet every second (the 70t), starting at 7 feet (the "7"), but is being drawn downward at a rate of -16t² feet/sec². I'm not clear this is a good equation for describing the ball's path, but it is what we are given. But please note that the ball rises at first, before gravity takes over and causes it to fall.

We want the time it takes to reach a height of 2 feet. So the equation becomes

2 = -16t²+ 70t +7, or

0 = -16t²+ 70t + 5

Solve for t using the quadratic formula. There should be two roots, one negative and one positive. Disregard the negative root, since that would mean a time before 0.

4.45 seconds, with a rough calculation.

Bob

I get around 4.