Chapter 9.2, Problem 6STP

A golf ball is driven in the air toward the hole from an elevated tee with an upward velocity of 160 ft/s. Its height $h$ in feet after $t$ second is given by the function $h=-16t^2+160t+18.$

How long will it take for the golf ball to reach its maximum height? What is the ball’s maximum height?

To determine

To find the time taken by golf ball to reach its maximum height. Find the ball’s maximum height.

Answer to Problem 6STP

The balls take 5 seconds to reach the maximum height. The ball’s maximum height is 418 ft.

Explanation of Solution

Given information: A golf ball is driven in the air towards the hole from an elevated tee with an upward velocity of 160 ft/s. Its height h in feet after t seconds is given by the function $h=-16t^2+160t+18$ .

Calculation: The solution is obtained as,

The maximum height corresponds to the vertex of the parabola which has an x-coordinate of: $x=-\frac{b}{2a}$

From the given, $a=169\&b=160$ so:

  $x=t=-\frac{160}{2\left(16\right)}=5$

The maximum height is reached at: $t=5$ seconds.

The maximum height is,

  $h=-16{\left(5\right)}^2+160\left(5\right)+18=418$ ft

Hence, the balls take 5 seconds to reach the maximum height. The ball maximum height is 418 ft.