(1090) Problem 7: Suppose that a 120 kg football plaver running at 8.5 ms catche
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Question
(1090) Problem 7: Suppose that a 120 kg football plaver running at 8.5 ms catches a 0.41 kg ball moving at a speed of 23.5 m/s with his feet off the ground, while both of them are moving horizontally. > 25% Part (a) Calculate the final speed of the player in meters per second, if the ball and player are initially moving in the same direction. Grade Summa Deductions Potential ry Vf,1 090 100% cos0 cotanasin0 tan() | Sin acosO atan acotan sinhO cotanhO Submissions Attempts remaining:J5 (5% per attempt) detailed view END Degrees Radians CLEAR Submit Hint I give up! Hints: 590 deduction per hint. Hints r emaining: Feedback: 5 % deduction per feedback. 25% Part (b) Calculate the change in kinetic energy of the system, in Joules, after the player catches the ball. 25% Part (c) Calculate the final speed of the player, in meters per second, if the ball and player are initially moving in opposite directions 25% Part (d) Calculate the change in kinetic energy ofthe system, in joules, in this caseExplanation / Answer
Given
Mass of the football player mp = 120 kg
Mass of the football mb = 0.41 kg
Velocity of the player vp = 8.5 m/s
Velocity of the ball vb = 23.5 m/s
Solution
1)
When the player and the ball are moving in the same direction,
Total momentum before collision = mpvp + mbvb
After the collision, since the player catched the ball, they both become one object and move with the same velocity
Total momentum after collision = (mp + mv)v
as per the conservation of momentum
Total momentum before collision = Total momentum after collision
mpvp + mbvb= (mp + mv)v
v = (mpvp + mbvb)/( mp + mv)
v = (120 x 8.5 + 0.41 x 23.5) / (120 + 0.41)
v = 8.55 m/s
2)
Initial kinetic energy = ½ mpvp2 + ½ mbvb2
Ei = ½ x 120 x 8.52 + ½ x 0.41 x 23.52
Ei = 4448.21125
Final kinetic energy = ½ (mp + mb)v2
Ef =½ (120+0.41) x 8.552
Ef = 4401.1360125
Energy Lost = Ei – Ef
E = 4448.21125 - 4401.1360125
E = 47.08 J
3)
When the player and the ball are moving in the opposite direction,
Total momentum before collision = mpvp - mbvb
After the collision, since the player catched the ball, they both become one object and move with the same velocity
Total momentum after collision = (mp + mv)v
as per the conservation of momentum
Total momentum before collision = Total momentum after collision
mpvp - mbvb= (mp + mv)v
v = (mpvp - mbvb)/( mp + mv)
v = (120 x 8.5 - 0.41 x 23.5) / (120 + 0.41)
v = 8.39 m/s
4)
Initial kinetic energy = ½ mpvp2 + ½ mbvb2
Ei = ½ x 120 x 8.52 + ½ x 0.41 x 23.52
Ei = 4448.21125
Final kinetic energy = ½ (mp + mb)v2
Ef =½ (120+0.41) x 8.392
Ef = 4237.9563805
Energy Lost = Ei – Ef
E = 4448.21125 - 4237.9563805
E = 210.25 J
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