Quadratic Word Problems

Question

A ball is thrown vertically upward with an initial velocity of 48 feet per second. If the ball started from a height of 8 feet off the ground, determine the time it will take for the ball to hit the ground.

Answer 1

The gravity descent formula is:

h(t) = -16t² + 48 t + 8

where the coefficient of the t² term is the acceleration due to gravity, the coefficient of the t term is the velocity of the item vertically, and the constant is the initial height.

h(t) = 0 when the item is at ground level. Using the quadratic formula,

t = 1 ± 0.5√6 seconds

So, approximately,

t = −0.224745 seconds

or

t = 2.22474 seconds

Since negative time makes no sense, the correct answer is the positive value for t.