A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x) = -1/25x( x – 45), where h(x) is the height of the golf ball and x is the horizontal distance it has traveled m. Solve the equation to determine how far the ball will have traveled when it hits the ground. How far will the ball need to roll to make it to the hole?

Answer 1

To determine how far the golf ball will have traveled when it hits the ground, we need to find the value of \( x \) when the height \( h(x) \) is equal to zero. The function given is:

\[ h(x) = -\frac{1}{25} x (x - 45) \]

Setting \( h(x) \) to zero, we have:

\[ -\frac{1}{25} x (x - 45) = 0 \]

This equation is satisfied when either factor on the right is zero:

1. \( x = 0 \)
2. \( x - 45 = 0 \) which gives \( x = 45 \)

The solutions indicate that the ball is at ground level at \( x = 0 \) (initial position) and \( x = 45 \) (when it hits the ground again).

So, the golf ball will have traveled \( 45 \) yards when it hits the ground.

Next, to determine how far the ball will need to roll to make it to the hole, we can calculate the distance from where the ball lands to the hole:

The hole is located \( 55 \) yards away from the start. Since the ball lands at \( 45 \) yards, the distance it needs to roll to reach the hole is:

\[ 55 - 45 = 10 \text{ yards} \]

Thus, the ball will need to roll 10 yards to make it to the hole.