Question

If a football is punted following the trajectory h(t)=-16t^2+71t+3, where h(t)* 1 pom

represents the height in feet over t seconds, determine h(3) and explain its
meaning in context.

Answer 1

To find the height of the football at 3 seconds, we need to substitute t = 3 in the given formula:

h(3) = -16(3)^2 + 71(3) + 3 = -144 + 213 + 3 = 72 feet

Therefore, the height of the football at 3 seconds is 72 feet.

The meaning of h(3) in context is that when the football has been in the air for 3 seconds, it will be at a height of 72 feet. According to the formula, the initial height of the football is 3 feet when it is punted or kicked. Hence, we can say that the ball was kicked from the ground, traveled upward and it will soon reach the ground again. This formula can be used to determine at what point the ball will hit the ground.

I hope this helps!