Question

A soccer player kicks the ball toward a goal that is 27.6 m in front of him. The ball leaves his foot at a speed of 18.5 m/s and an angle of 31.2° above the ground. Find the speed of the ball when the goalie catches it in front of the net. (Note: The answer is not 18.5 m/s.)

I keep getting a final velocity of 13.92797m/s but its incorrect. Please show your work so I can see what I'm doing wrong.

Answer 1

Initial velocity of the ball,

Initial vertical velocity,

Initial horizontal velocity,

Distance to goal,

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First, find the time of flight

Consider the horizontal motion of the ball

There is no acceleration in the horizontal direction, so horizontal velocity remains a constant

Horizontal velocity = Horizontal Distance/Time of flight

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Consider the vertical motion of the ball

Use formula

Initially, the ball is going up and g is acting downwards, so put a negative sign for g

Note: Negative sign just indicates that the ball is falling

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Consider the horizontal motion of the ball

There is no acceleration in the horizontal direction, so horizontal velocity remains a constant

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Final velocity,

ANSWER :

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