Question

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. 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 25 yards. It will need to roll an additional 30 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.

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.

Answer 1

To determine how far the ball travels before it hits the ground, we solve the equation:

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

Setting the equation equal to zero, we can factor it:

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

This gives us two solutions:

1. \( x = 0 \) (the starting point)
2. \( x - 45 = 0 \) or \( x = 45 \)

So the ball will hit the ground when it has traveled **45 yards**.

Now, to find out how far it will roll to reach the hole, we subtract the distance traveled from the hole's distance:

\[
\text{Distance to the hole} = 55 \text{ yards}
\]
\[
\text{Rolling distance} = 55 \text{ days} - 45 \text{ yards} = 10 \text{ yards}
\]

Thus, the golf ball will hit the ground after it has traveled **45 yards** and will need to roll an additional **10 yards** to reach the hole.

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.**