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 ty,max for t, 0 for yi, and h for yf, and gets

h = 

vi2 sin2 ?i
2g

 

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

what angle results in the maximum horizontal range=45° 

I substituted

2vi sin ?i
g
into the expression for the horizontal component of velocity, (vi cos ?i)t, and got 
R = 
2vi2 sin ?i cos ?i
g

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

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