Sam Bradford throws a football to Stefon Diggs while standing at the center of a

Question

Sam Bradford throws a football to Stefon Diggs while standing at the center of a field on the 50 yard line. The ball leaves his hand at a height of 6 feet and initial velocity v_0 = 40i + 35j + 32k ft/s. Assume an acceleration of 32 ft/s^2 due to gravity with the i vector pointing towards the end zone, j vector towards the sideline, and the field is 150 ft wide and 300 ft long. If Diggs catches the ball 6 feet above the ground, will he be in bounds? If not, how high would he need catch the ball in order to stay in bounds?

Explanation / Answer

given V= 40i +35 j + 32k

i represents end zone

j represents side line

k represents vertically down direction.

since ball leaves hand at 6 ft and is received at 6 ft, so net vertical displacement =0.

using newtons law in vertical direction

s= ut + (1/2)at2

0= 32 t + (1/2) (-32) t2

solving we get t=0 and t=2.

since he is throwing from centre.

ground distance in i direction is 75 ft.

distance travelled by ball in i direction = 40 x 2 =80. ( Not in bounds)

ground distance in j direction is 150 ft.

distance travelled by ball in j direction = 35 x 2 =70. ( In bounds)

In i direction, to be in bounds,

40 x t = 75

t= 1.875

s= 32(1.875) - (1/2) (32) (1.8752)

=3.75

he should catch 6 + 3.75 = 9.75 feet above ground.

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