Question

A football is punted from a height of 3.5 feet about the ground with an initial velocity of 45 feet per second. This situation can be represented by the function h(t)=- 16t^2 + 45t + 3.5, where t is the number of seconds elapsed since the football was kicked. If the football is caught at a height of 5.5ft on the ball's descent, how long was the football in the air? Round to the nearest hundredth.
*show me how you did it not just the answer please​

Answer 1

The time at which the ball was in the air for the two cases of being dropped and being caught are respectively; t = 0.05 s and t = 2.77 s

What was the time of descent?

We are given the function to represent the given height as;

h(t)= -16t² + 45t + 3.5

Since the football is caught at a height of 5.5ft on the ball's descent, then;

-16t² + 45t + 3.5 = 5.5

⇒ -16t² + 45t - 2 = 0

From online quadratic equation solver, we have;

t = 0.05 s and t = 2.77 s

Read more about projectile motion at; https://brainly.com/question/11049671