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)

Question

, where h(x)
is the height of the golf ball and x is the horizontal distance it has traveled. 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?

0=−1/25x(x−45)


(1 point)
Responses

The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.
The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.

The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.
The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.

The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.
The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.

The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.

Answer 1

To determine how far the ball travels when it hits the ground, we need to solve the equation for \( h(x) = 0 \):

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

This equation will be zero when either \( x = 0 \) or \( x - 45 = 0 \).

1. Finding the roots:
   • From \( x = 0 \), the ball is at the initial position.
   • From \( x - 45 = 0 \), we find \( x = 45 \).

Thus, the ball will hit the ground after it has traveled 45 yards.

2. Determining how far it needs to roll to reach the hole: The hole is 55 yards away, and the ball travels 45 yards to the ground, leaving:

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

Therefore, the ball will need to roll an additional 10 yards to reach the hole.

So, the correct response is:

The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.