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?%0D%0A%0D%0A0=−1/25x(x−45) %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.%0D%0AThe ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.%0D%0A%0D%0AThe ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.%0D%0AThe ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.%0D%0A%0D%0AThe ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.%0D%0AThe ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.%0D%0A%0D%0AThe ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.

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?%0D%0A%0D%0A0=−1/25x(x−45) %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.%0D%0AThe ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.%0D%0A%0D%0AThe ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.%0D%0AThe ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.%0D%0A%0D%0AThe ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.%0D%0AThe ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole.%0D%0A%0D%0AThe ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.

GPT-4o mini · Answer

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

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

Setting the equation to zero gives us two possible solutions:

\( x = 0 \) (the starting point)
\( x - 45 = 0 \) which gives \( x = 45 \)

These solutions indicate that the ball hits the ground at two points: 1) when it is hit (at \( x = 0 \)) and 2) when it reaches another point on its parabolic path, which is at \( x = 45 \) yards horizontally.

Now, since the hole is 55 yards away and the ball hits the ground at 45 yards, we can determine how far it will need to roll:

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

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.