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the function A goffer hits a golf ball toward the hole 55 yards away. The Isall follows a parabolic path given by h(x)=- 1/25 x(x-45) where h(x) us the height of the golf ball and x is the horizontal distance it has traveled. Solve the equation to determise how far the ball will have traveled when it hits the ground. How far will the hall need to roll to make it to the hole? 0=- 1/25 x(z-45) (2 point) to reach the hol The hall will hit the gozund aher it has iraveled 45 yoods. It will need to soll an additional 10 yards to reack the hole. The ball will h't the groued after it has traveled 30 yaeds. It will meed tn mll an additional 25 yaud s ho teach the hol The hall will hi the ground after is has traveled 1D yards. It will need to sll an addiional 45 yards to reach the hol The ball will hit the ground aftor it has traveed 25 yards. It will need to sall as additional 30 yands

1 answer

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

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

Setting \( h(x) \) to zero gives us:

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

Multiplying both sides by -25 to eliminate the negative fraction:

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

This equation factors to:

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

Setting each factor to zero, we get:

  1. \( x = 0 \)
  2. \( x - 45 = 0 \) → \( x = 45 \)

This tells us that the golf ball hits the ground after it has traveled 45 yards.

Next, we need to determine how far the ball will roll to reach the hole, which is 55 yards away from its starting point. Since the ball travels 45 yards before hitting the ground, the distance it needs to roll to reach the hole is:

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

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.

So, the answer is that 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.