The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 12 m/s at an angle 47 degrees

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 12 m/s at an angle 47 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters above the ground.

1)What is the horizontal component of the ball’s velocity when it leaves Julie's hand? 

2)What is the vertical component of the ball’s velocity when it leaves Julie's hand? 

3)What is the maximum height the ball goes above the ground?

4)What is the distance between the two girls?

 

5)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 10 m/s when it reaches a maximum height of 8 m above the ground.What is the speed of the ball when it leaves Sarah's hand?

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

 

Answer 1

g = -9.8 m/s², v_h is constant, v_vf = 0, h_i = 1.5 m

1.     horizontal component (v_h)= (12 m/s)(cos 47°) = 8.2 m/s

2.     vertical component (v_vi)= (12 m/s)(cos 47°) = 8.8 m/s

3.     Use v_vf = v_vi + gt to get time to the highest point then double to get total time in the air; 0 = 8.8 + (-9.8)t; t = 0.9 s; t_air = 1.8 s

Use final height (h_f) = initial height (h_i) + v_vi t = 0.5gt²; h_f = 1.5 + 8.8(.9) + 0.5(-9.8)(.9)²; h_f = 5.5 m

4.     Use v_h = d/ t_air; 8.2 = d/1.8; d = 15 m

5.     Use v_vf² = v_vi² + 2gh with h = 8 – 1.5 = 6.5 m; 0 = v_vi² + 2(-9.8)(6.5); v_vi² = 127.4; v_vi = 11 m/s

Use Pythagorean theorem with horizontal and vertical components to get velocity of the throw; v² = 11² + 10²; v = 15 m/s

6.     They are 15 m apart so it takes 1.5 seconds (horizontal velocity is constant 10 m/s) to gets to Julie

Use final height (h_f) = initial height (h_i) + v_vi t = 0.5gt²; h_f = 1.5 + 11(1.5) + 0.5(-9.8)(1.5)²; h_f = 7 m (way over her head!)