In order to win the game, a placekicker must make a field goal from a distance o

Question

In order to win the game, a placekicker must make a field goal from a distance of 42.0 m. The regulation height for the crossbar is 2.44 m and, after making a back of the helmet calculation, the placekicker decides to kick the ball with a speed of 26.0 m/s at an angle of 54.1° with respect to the horizontal (a) Determine the amount by which the ball clears or falls short of clearing the crossbar. Enter a negative value if the ball falls short (b) Determine if the ball is rising or falling as it approaches the crossbar. rising falling

Explanation / Answer

a)

Initial Horizontal and vertical components of velocities are

Vox=26Cos54.1

Voy=26Sin54.1

Horizontal distance travelled

X=Voxt

42=(26Cos54.1)t

t=2.755 s

From

Y=Yo+Voyt-(1/2)gt2

Y=(26Sin54.1)(2.755) -(1/2)(9.81)(2.755)2

Y=20.8 m

Therefore the ball clears the post is

H=20.8-2.44 =18.36 m

b)

From

Vfy=Voy-gt

at maximum height Vfy=0

=>0 =(26Sin54.1)-9.81t

t=2.147 s

Therefore the ball is falling when it approaches the crossbar

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