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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) (1 point) Responses 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. 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 10 yards. It will need to roll an additional 45 yards to reach the hole.

1 answer

To find out how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \):

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

This equation can be set to zero for values of \( x \):

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

The product \( x(x - 45) \) must equal zero. This gives us:

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

This means the ball hits the ground after it has traveled either \( 0 \) yards (the starting point) or \( 45 \) yards. Therefore, the ball will hit the ground after it has traveled 45 yards.

Since the hole is 55 yards away, we now determine how far the ball will need to roll to reach the hole:

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

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

Putting this together, the 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.