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 crossba (a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer if it falls short.) 0 It may be helpful to first determine the time required for the ball to reach the goal, m (b) Does the ball approach the crossbar while still rising or while falling? rising falling
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 crossba (a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer if it falls short.) 0 It may be helpful to first determine the time required for the ball to reach the goal, m (b) Does the ball approach the crossbar while still rising or while falling? rising falling
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Transcribed Image Text: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 20.2 m/s at an angle of 47.0° to the horizontal.
(a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer if it falls short.)
0
X
It may be helpful to first determine the time required for the ball to reach the goal. m
(b) Does the ball approach the crossbar while still rising or while falling?
O rising
O falling
Expert Solution
Step 1: Concept and given details
Gravitational acceleration = g = -9.81 m/s2
Initial velocity of the ball = V0 = 20.2 m/s
Angle at which the ball is kicked = (θ) = 47°
Initial horizontal velocity of the ball = Vx0 = V0Cos(θ) = (20.2)Cos(47) = 13.78 m/s
Initial vertical velocity of the ball = Vy0 = V0Sin(θ) = (20.2)Sin(47) = 14.77 m/s
Distance of the crossbar from the initial position of the ball = R = 36 m
Height of the crossbar = H0 = 3.05 m
Time taken by the ball to reach the crossbar = T
There is no horizontal force on the ball therefore the horizontal acceleration is zero.
R = Vx0T
36 = (13.78)T
T = 2.61 sec
Height of the ball when it reaches the crossbar = H1
H1 = Vy0T + gT2/2
H1 = (14.77)(2.61) + (-9.81)(2.61)²/2
H1 = 5.14 m
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