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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)

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. - not selected, this is the correct answer

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. - no response given

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. - incorrect

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.

1 answer

To solve the equation \(0 = -\frac{1}{25}x(x - 45)\), we will start by setting the equation equal to zero and solving for \(x\).

  1. Set the equation to zero: \[ 0 = -\frac{1}{25}x(x - 45) \]

  2. Multiply both sides by \(-25\) to eliminate the fraction: \[ 0 = x(x - 45) \]

  3. Factor the equation: \[ 0 = x(x - 45) \]

This gives two solutions:

  • \(x = 0\) (the starting point)
  • \(x = 45\) (where the ball hits the ground)

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

  1. Calculate how far the ball needs to roll to reach the hole: The hole is 55 yards away. Since the ball travels 45 yards before hitting the ground, the distance it needs to roll is: \[ 55 - 45 = 10 \text{ yards} \]

In conclusion:

  • 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 correct answer 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.