A golf ball is struck by a 60-degree golf club at an initial velocity of 96 feet

Question

A golf ball is struck by a 60-degree golf club at an initial velocity of 96 feet per second. The height of the golf ball in feet is given by the quadratic function h(x) = 16x^2/(48)^2 + 83.1/48 x, where x is the horizontal distance of the golf ball from the point of impact. What is the horizontal distance of the golf ball from the point of impact when the ball is at its maximum height? What is the maximum height obtained by the golf ball? The horizontal distance of the golf ball from the point of impact when the ball is at its maximum height is feet. (Round to two decimal places as needed) The maximum height obtained by the golf ball is feet. (Round to two decimal places as needed.)

Explanation / Answer

To find the horizontal distance and the maximum height, we have to just find the vertex,

x = -b/2a

We have b = 83.1/48

We have a = -16/ 482   

Now, -b/2a = -(83.1/48) / (2) (-16/ 482 ) = 124.65

So, horizontal distance of golf ball from the point if impact when the ball is at it's maximum height is 124.65 ft (ANSWER)

Now, we have to plug 124.65 back into the quadratic function given to us in the problem.

So,

-16(124.652) / (482) + (83.1)(124.65) / 48 = 107.90

So, the maximum height obtained by the golf ball is 107.90 ft (ANSWER)

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