A golfer on a level fairway hits a ball at an angle of 25° to the horizontal that travels 103 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 103 yd. At what angle was the second ball hit? (Neglect air resistance.)

Question

A golfer on a level fairway hits a ball at an angle of 25° to the horizontal that travels 103 yd before striking the ground. He then hits another ball from the same spot with the same speed, but at a different angle. This ball also travels 103 yd. At what angle was the second ball hit? (Neglect air resistance.)

Answer 1

range = [(launch velocity)^2 * sin(twice the launch angle)] / g

when you solve for the launch angle , you will see two solutions

Answer 2

To solve this problem, we can use the fact that the horizontal component of the velocity remains constant and the vertical component of the velocity changes due to gravity.

Let's break down the given information:

- The first ball is hit with an angle of 25° to the horizontal and travels 103 yards before hitting the ground.
- The second ball is hit from the same spot with the same initial speed and travels the same distance of 103 yards.

We need to find the angle at which the second ball was hit.

To solve this problem, we can use the following equations of motion:

1. Horizontal component of velocity (Vx): Vx = V * cos(theta)
2. Vertical component of velocity (Vy): Vy = V * sin(theta)
3. Time of flight (t): t = (2 * Vy) / g
4. Horizontal range (R): R = Vx * t

We can use the above equations to set up a system of equations:

For the first ball:
V1x = V1 * cos(25)
V1y = V1 * sin(25)
t1 = (2 * V1y) / g
R1 = V1x * t1

For the second ball:
V2x = V2 * cos(theta)
V2y = V2 * sin(theta)
t2 = (2 * V2y) / g
R2 = V2x * t2

Since we are given that the range (R1) and (R2) are the same for both balls, we can equate them:
V1x * t1 = V2x * t2

We also know that V1x = V1 * cos(25) and V2x = V2 * cos(theta).
Substituting these values in the equation above, we get:
(V1 * cos(25)) * (2 * V1 * sin(25) / g) = (V2 * cos(theta)) * (2 * V2 * sin(theta) / g)

Simplifying the equation, we get:
cos(25) * sin(25) = cos(theta) * sin(theta)

Now, to find the value of theta, we can take the inverse sine (sin^-1) of both sides, which gives us:
theta = sin^-1(sin(25) * cos(25))

Evaluating this expression using a calculator, we find that the angle at which the second ball was hit (theta) is approximately 65.017 degrees.

Therefore, the second ball was hit at an angle of approximately 65.017 degrees to the horizontal.