Question

A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 22.4 m/s at an angle of 47.0° to the horizontal. (a) By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.) m (b) Does the ball approach the crossbar (and cross above or beneath it) while still rising or while falling?

Answer 1

Initial velocity ,

First find Range

The ball will be rising from 0m to 25.51m (R/2) ,then falling till 51.02m

Since the goal is 36m from point of launching,the Ball will be falling when it approaches the crossbar

(b)ANSWER: Falling.

(a)Horizontal distance to goal = 36m

Since there no acceleration in horizontal direction

Horizontal speed =Horizontal distance/time

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Time of flight,

so time to reach max height ,

Time taken to reach goal after reaching max height

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Max Height

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Consider the vertical motion, Falling Part

Use formula

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Distance From ground,

The ball will at a height of 10.14m when it is above the goal

(a)ANSWER: The ball will clear the goal by 7.09m.

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