A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x)=− 1/25 x(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=− 1/25 x(x−45)

(1 point)
Responses

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.
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 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 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.

Answer 1

To determine how far the golf ball travels before hitting the ground, we need to solve the equation given by the height function \( h(x) = -\frac{1}{25} x(x-45) \) for when \( h(x) = 0 \).

Set the equation equal to zero:

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

Multiplying both sides by \(-25\) gives us:

\[ 0 = x(x - 45) \]

This factored equation means we will have solutions when either factor equals zero:

1. \( x = 0 \) (this is the starting point)
2. \( x - 45 = 0 \) which gives \( x = 45 \)

So the ball hits the ground when \( x = 45 \) yards.

Now, we need to find out how far the ball will need to roll to reach the hole, which is 55 yards away. The distance that the ball still needs to cover after hitting the ground is given by:

\[ \text{Distance to roll} = \text{Distance to hole} - \text{Distance traveled} = 55 - 45 = 10 \text{ yards}. \]

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

Thus, 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.