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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A placekicker 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 20.0 m/s at an angle of 53.0° to the horizontal, (a) By how much does the ball clear or fall short of clearing the crossbar? (b) Does the ball approach the crossbar while still rising or while falling?

(a)

To determine
By how much does the ball clear or fall short of clearing the crossbar.

Explanation

The time required to travel the horizontal distance is,

t=xv0x=xv0cosθ

  • x is the horizontal distance
  • v0 is the initial velocity
  • θ is the angle of projection

The vertical displacement of the ball is,

y=v0yt+12ayt2

The vertical distance by which the ball clears the bar is,

d=yh=v0yt+12ayt2h=v0sinθ(xv0cosθ)+12ay(xv0cosθ)2h

Conclusion:

The vertical distance by which the ball clears the bar is,

d=v0sinθ(xv0cosθ)+12ay(xv0cosθ)2h

Substitute 53

(b)

To determine
If the ball approaches the crossbar while still rising or while falling.

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