Question

Homework Problem Set 06 Student Name 70. A 60-kg soccer player jumps vertically upwards and heads the 0.45-kg ball as it is descending vertically with a speed of 25 m/s. If the player was moving upward with a speed of 4.0 m/s just before impact, what will be the speed of the ball immediately after the collision if the ball rebounds vertically upwards and the collision is elastic? If the ball is in contact with the player's head for 20 ms, what is the av- erage acceleration of the ball? (Note that the force of grav- ity may be ignored during the brief collision time.)

Answer 1

To solve this problem, we can apply the principle of conservation of momentum in an elastic collision. The speed of the ball immediately after the collision can be calculated using the principle of conservation of momentum. The average acceleration of the ball can be calculated using the formula for average acceleration.

Step-by-step explanation:

To solve this problem, we can apply the principle of conservation of momentum in an elastic collision. Since the collision is elastic, the total momentum before and after the collision remains the same. The momentum is given by the product of mass and velocity. Before the collision, the player's mass doesn't affect the speed of the ball, so we can ignore it. The initial momentum of the ball is the product of its mass and velocity. After the collision, the ball rebounds vertically upwards with a certain velocity. We can use the principle of conservation of momentum to calculate this velocity.

The average acceleration of the ball during the collision can be calculated using the formula for average acceleration: average acceleration = change in velocity / time. In this case, the change in velocity is the difference between the ball's final velocity after the collision and its initial velocity before the collision, and the time is given as 20 ms. By substituting these values into the formula, we can find the average acceleration of the ball during the collision.

Answer 2

The average acceleration of the ball is 2,105 m/s² upwards.

How to calculate the average acceleration of the ball?

The average acceleration of the ball is calculated by applying the following formula as shown below;

a = (v - u)/t

where;

• u is the initial speed of the ball
• t is time of action
• v is the final speed of the ball

The final speed of the ball after the impact is calculated using conservation of linear momentum as follows;

60 x 4 - 0.45 x 25 = 60v₁ + 0.45v₂

228.75 = 60v₁ + 0.45v₂

508.33 = 133.33v₁ + v₂ ------- (1)

v₁ + 4 = v₂ + 25

v₁ = v₂ + 21 -------- (2)

508.33 = 133.33v₁ + v₂

508.33 = 133.33 (v₂ + 21) + v₂

508.33 = 133.33v₂ + 2,799.93 + v₂

-2291.6 = 134.33v₂

v₂ = -17.1 m/s

so the direction of the final velocity of the ball is in opposite direction.

The average acceleration of the ball is calculated as;

a = (- 17.1 - 25 )/ 0.02 s

a = - 2,105 m/s²