A football is kicked on level ground towards the goal with a

A football is kicked on level ground towards the goal with a velocity of 20m/s at an angle of 38.67 degree with the horizontal. The goal is 36m and the crossbar is 3m high. Find the time it takes for the ball to reach the goal. Find the height of the ball when it reaches the goal. Does it pass above or below the crossbar? How far past the goal (the distance d in the diagram) does the ball land?

Solution

Vo = 20 m/sec at 38.67 deg from horizontal

Vox = 20*cos 38.67 deg = 15.61 m/sec

Voy = 20*sin 38.67deg = 12.49 m/sec

range = 36 m

height of post = 3 m

Range of projectile motion is given by

R = V0^2*sin 2A/g

R = 20^2*(sin 77.34 deg)/9.81 = 39.78 m

Time of flight = T = 2*Vo*sin A/g

T = 2*20*(sin 38.67 deg)/9.81 = 2.55 sec

max height = H = Vo^2*(sin A)^2/2g

H = 20^2*(sin 38.67 deg)^2/(2*9.81) = 7.95 m

A.

time for ball to reach the goal

X = V0*cos A*t

X = 36 m given

t = X/V0*cos A

t = 36/(20*cos 38.67 deg) = 2.305 sec

B.

y = y0 + Voy*t - 0.5*g*t^2

y = 0 + 12.49*2.305 - 0.5*9.81*2.305^2 = 2.729 m

So ball will go below the post.

C.

range of projectile = 39.78 m

range of goal = 36 m

d = 39.78 - 36 = 3.78 m