Julie throws a ball to her friend Sarah. The ball leaves Julie\'s hand a distanc

Question

Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 10 m/s at an angle 36 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters above the ground.

1- After catching the ball, Sarah throws it back to Julie. The ball leaves Sarah's hand a distance 1.5 meters above the ground, and is moving with a speed of 11 m/s when it reaches a maximum height of 5 m above the ground.

What is the speed of the ball when it leaves Sarah's hand?

2-How high above the ground will the ball be when it gets to Julie? (note, the ball may go over Julie's head.)

Explanation / Answer

1) lets find vertical speed of the ball when it leaves Sarah's hand

v2 = u2 -2gh

here v=0, g=9.8m/s2, h=5-1.5=3.5m, u=vertical speed

0=u2 - 2*9.8*3.5

u=8.28 m/s

horizontal speed = 11m/s

total speed = sq. root of ( 112 +8.282) = 13.77 m/s Answer

2) lets find the horizontal distance between Sarah and Julie

Range =Vo2 sin(2*36o) /g = 100*0.951/9.8 = 9.7 m

time taken to reach to Julie = horizotal range/ hor. speed= 9.7/ 11 = 0.882s

height of the ball (above 1.5m) at this point of time = ut -0.5gt2 = 8.28*0.882 - 0.5*9.8*0.882*0.882

= 3.5 m

total height above ground when it gets to Julie =3.5 +1.5 = 5 m Answer

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