Calculating the Maximum Height and Range of a Tennis Ball

Now Abel and Kato use what they learned to answer the following problem

The initial speed of a tennis ball is 55 m/s and the launch angle is 01=29∘. Neglect air resistance. What is the maximum height, h, of the tennis ball? mi What is the range, R, of the tennis ball?

Final answer: To find the maximum height, use the formula h = (v_y0)^2 / (2g), with v_y0 = v_0 * sin(θ). The maximum height is approximately 16.67 m. To find the range, use the formula R = v_0 * cos(θ) * t, where t is the time of flight. The range is approximately 212.38 m.

Explanation:

To find the maximum height, we need to use the kinematic equations of motion. The initial vertical velocity can be found using the launch angle and the initial speed. Using the formula vy0 = v0sin(θ), we get vy0 = 55 m/s * sin(29°). The maximum height can be found using the formula h = (vy0)2 / (2g), where g is the acceleration due to gravity. Plugging in the values, we get h ≈ 16.67 m.

To find the range, we can use the time of flight, which is the time it takes for the ball to reach the ground. The formula for the time of flight is t = 2vy0 / g. Plugging in the values, we get t ≈ 4.15 s. The range can be found using the formula R = v0 * cos(θ) * t. Plugging in the values, we get R ≈ 212.38 m.