A rookie quarterback throws a football with an initial upward velocity component

Question

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. How much time is required for the football to reach the highest point of the trajectory? How high is this point? How much time (after it is thrown) is required for the football to return to its original level? How does this compare with the time calculated in part (a)? How far has the football traveled horizontally during this time? Draw x-t, y-t, upsilon_x-t, and upsilon_y-t graphs for the motion.

Explanation / Answer

a)

The time of ascent is given by

ta =vy/g =12m/s/9.81m/s2 =1.223s

b)

The maximum height reached is

H =Vy2/2g =(12)2/2*9.81 =1.223m

c)

The total time of flight is T =2ta =2*1.223=2.446s

d)

The distance travelled horizintally is given by

d =horizontal component of velocity*time of flight

=20m/s*2.446s =48.92m

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