Now Abel and Kato Solve a Tennis Ball Problem
Determining the Maximum Height of the Tennis Ball
The maximum height, h, of a projectile can be calculated using the formula:
h = (v₀sinθ)² / (2g)
Where:
v₀ = initial speed of the projectile (52.4 m/s)
θ = launch angle (28°)
g = acceleration due to gravity (9.8 m/s²)
Plugging in the given values:
h = (52.4 m/s * sin 28°)² / (2 * 9.8 m/s²)
h = (52.4 * 0.469)² / 19.6
h = 56.4 meters (to three significant figures)
Calculating the Range of the Tennis Ball
The range, R, of a projectile can be determined using the formula:
R = (v₀² * sin2θ) / g
Substitute the known values:
R = (52.4 m/s)² * sin(2 * 28°) / 9.8 m/s²
R = (52.4)² * sin(56°) / 9.8
R = 200 meters (to three significant figures)
Therefore, the maximum height of the tennis ball is 56.4 meters, and the range is 200 meters.