A soccer ball is kicked with an initial horizontal velocity

A soccer ball is kicked with an initial horizontal velocity of 11 m/s and an initial vertical velocity of 16 m/s. What is the initial speed of the ball? m/s What is the initial angle theta of the ball with respect to the ground? degrees What is the maximum height the ball goes above the ground? m How far from where it was kicked will the ball land? m What is the speed of the ball 2 seconds after it was kicked? m/s How high above the ground is the ball 2 seconds after it is kicked? m

Solution

a) Initial speed = sqrt (11² + 16²)

= 19.42 m/s

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b) v cos theta =11 m/s, v sin theta =16 m/s

v sin theta / v cos theta = 16 / 11

tan theta = 1.45

theta = 55.41 deg

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c) Max height = v sin theta² / 2 g =16² / ( 2 * 9.8 )

= 13.06 m

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d) Range = v² sin 2theta / g

= 19.42² * sin (2 * 55.41) / 9.8

= 35.98 m