A golf ball is hit with an initial angle of 30.5° with respect to the horizontal and an initial velocity of 81.9 mph. It lands a distance of 86.8 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?
Write an ideal (zero resistance) equation for vertical height vs time and compute the time and location where the ball lands (Z = 0). Compare that with the actual distance where it lands.
Is that ball speed really miles per hour or meters per second? If it is mph, convert the speed to meters per second before doing the problem.
86.8 meters is not a very long golf shot. If the ball is only hit at 30.5 degrees to horizontal, the wrong golf club choice was probably made
To determine how much the effects of wind resistance, spin, and other factors reduced the range of the golf ball from the ideal value, we first need to calculate the ideal range.
The ideal range of a projectile can be calculated using the following formula:
Range = (velocity^2 * sin(2 * angle)) / gravity
Where:
- Range is the horizontal distance traveled by the projectile
- Velocity is the initial velocity of the projectile
- Angle is the launch angle with respect to the horizontal
- Gravity is the acceleration due to gravity
Let's plug in the given values and calculate the ideal range:
Angle (θ) = 30.5°
Velocity (v) = 81.9 mph = 36.56 m/s (convert mph to m/s)
Gravity (g) = 9.8 m/s^2
Range_ideal = (36.56^2 * sin(2 * 30.5)) / 9.8
Now we can calculate the ideal range:
Range_ideal = (1335.0736 * 0.997) / 9.8
Range_ideal ≈ 136.52 m
The ideal range of the golf ball is approximately 136.52 meters.
To find the reduction in range due to external factors, we subtract the actual range from the ideal range:
Reduction in range = Range_ideal - Actual range
Actual range = 86.8 m
Reduction in range = 136.52 - 86.8
Reduction in range ≈ 49.72 m
Therefore, the effects of wind resistance, spin, and other factors reduced the range of the golf ball from the ideal value by approximately 49.72 meters.