From what height, in feet, was the ball dropped? After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?

Question

the quadratic function h(t)=-16.1t²+150 models a basketballs height, in feet,over time,in seconds, after it is dropped from a 15 story building. From what height, in feet, was the ball dropped? After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?

Answer 1

In order to find height from where ball is dropped, you have to find height or h(t) when time or t is zero.

So plug in t=0 into your quadratic equation:

h(0) = -16.1(0^2) + 150

h(0) = 0 +150

h(0) = 150 ft is the height from where ball is dropped.

 

When ball hits the ground, the height is zero. So plug in h(t) = 0 and solve for t.

0 = -16.1t^2 + 150

16.1 t^2 = 150

t^2 = 150/16.1

t = sqrt(150/16.1)

t = ± 3.05

Since time cannot be negative, your answer is positive solution i.e. t = 3.05