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.