The initial speed of a tennis ball is 57.5 m/s and the launch angle is ?i = 16°. Neglect air resistance. Question 1) What is the maximum height, h, of the tennis ball? in m Questione 2) What is the range, R, of the tennis ball? in m

The initial speed of a tennis ball is 57.5 m/s and the launch angle is ?i = 16°. Neglect air resistance. Question 1) What is the maximum height, h, of the tennis ball? in m Questione 2) What is the range, R, of the tennis ball? in m

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The initial speed of a tennis ball is 57.5 m/s and the launch angle is ?_i = 16°. Neglect air resistance.

Question 1) What is the maximum height, h, of the tennis ball? in m
Questione 2) What is the range, R, of the tennis ball? in m

info given: what angle results in the greatest height=90 For this 90° angle, the horizontal component of velocity is zero, so the initial velocity is completely in the vertical direction, resulting in greatest height

Kato tries substituting t_y,maxfor t, 0 for y_i, and h for y_f, and gets

h =

v_i² sin² ?_i

When ?_i = 90°, sin² ?_i is maximum, so h is maximum

what angle results in the maximum horizontal range=45°

I substituted

2v_i sin ?_i

into the expression for the horizontal component of velocity, (v_i cos ?_i)t, and got

R =

2v_i² sin ?_i cos ?_i

when ?_i = 45°, 2?_i = 90°, and sin 90° = 1, which is its maximum value.

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