Question

A football is kicked up from ground level at an initial upward velocity of 80 ft./s. The equation h=-16t^2 + 80t give the height h of the football after t seconds. What are realistic values for t?

Answer 1

Explanation:

Note that the given height equation, which is a quadratic) has a graph that opens downward. Borrowing the quadratic formula, we find the roots of this equation, that is, the t values at which h(t) = 0:

The coefficients of this equation are a = -16, b = 80 and c = 0.

We need to find the roots of this quadratic. By the quadratic formula,

-(80) ±√(80² - 4(-16)(0) ) -80 ± 0

t = ------------------------------------- = ----------------- = -5/2 and -5/2 (seconds).

2(-16) -32

The initial height is 0 at t = 0 seconds and the final height 0 at 5/2 seconds.