Answer:

A football is kicked at an angle of 37 degrees with a velocity of 20 m/s.

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You didn't spec the Earth's gravitational acceleration.

I'll use 10 m/sec/sec

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Calculate:

a.) Maximum height

Vertical component Vv = 20*sin(37) =~ 12.036 m/sec

Flight time = 12.036*2/10 = 2.407 seconds

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h(t) = -5t^2 + 12.036t

Max is the vertex @ t = -b/2a = 12.036/10 = 1.2036 seconds

h(1.2036) = 7.243 meters Max height

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b.) The time of travel before the ball hits the ground

2.407 seconds

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c.) The range

Horizontal component = 20*cos(37) =~ 15.973 m/sec

range = 15.973*2.407 = 38.45 meters

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d.) The velocity vector at the maximum height

= Horizontal component at angle zero (no vertical speed)

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e.) The acceleration vector at the maximum height

= -5 m/sec/sec at all times