A golf ball is hit with an initial angle of 54.7o with respect to the horizontal and an initial velocity of 85.1 mph. It lands a distance of 104.3 m away from where it was hit. By how much did the effects of wind resistance, spin, and so forth reduce the range of the golf ball from the ideal value?

The ideal range is

(Vo^2/g)*sin(2*54.7)

Subtract 104.3 m from that for the answer.

You will have to convert 104.3 mph to m/s before applying the formula.

That is an extremely slow speed for a golf ball. A reasonably healthy person can throw a golf ball at that speed.

I meant 85.1 mph for the speed that must be cnverted to m/s

To calculate the reduction in range of the golf ball due to the effects of wind resistance, spin, and other factors, we need to compare the actual range with the ideal range. The ideal range is the theoretical distance the ball would have traveled in the absence of any external influences.

1. Convert the initial velocity from mph to m/s:
85.1 mph = 38.04 m/s

2. Split the initial velocity into its horizontal and vertical components:
Horizontal component (Vx) = V₀ * cos(θ)
Vertical component (Vy) = V₀ * sin(θ)
where V₀ is the initial velocity and θ is the launch angle.

Vx = 38.04 m/s * cos(54.7°)
= 20.04 m/s
Vy = 38.04 m/s * sin(54.7°)
= 29.94 m/s

3. Calculate the time of flight (t):
Use the equation: t = (2 * Vy) / g
where g is the acceleration due to gravity (9.8 m/s²).

t = (2 * 29.94 m/s) / 9.8 m/s²
≈ 6.09 s

4. Calculate the ideal range (R_ideal):
Use the equation: R_ideal = Vx * t

R_ideal = 20.04 m/s * 6.09 s
≈ 122.16 m

5. Calculate the reduction in range:
Reduction in range = R_ideal - 104.3 m
= 122.16 m - 104.3 m
= 17.86 m

Therefore, the effects of wind resistance, spin, and other factors reduced the range of the golf ball by approximately 17.86 meters from the ideal value.