An 80- kg quarterback jumps straight up in the air right before throwing a 0.43-kg football horizontally at 15m/s . Sort the following quantities as known or unknown. a. Take the horizontal direction to be along the x axis. : b. the mass of the quarterback, : the mass of the football, : c. the horizontal velocity of quarterback before throwing the ball, : d. the horizontal velocity of football before being thrown, : e. the horizontal velocity of quarterback after throwing the ball, : the horizontal velocity of football after being thrown

1. The mass of the quarterback = known = 80 kg

2. The mass of the football = known = 0.43 kg

3. The horizontal velocity of quarterback before throwing the ball = known = 0

4. The horizontal velocity of football before being thrown = known = 0

5. The horizontal velocity of quarterback after throwing the ball, = unknown quantity and it can be calculated using the conservation of linear momentum.

6. The horizontal velocity of football after being thrown = known = 15 m/s

Explanation:

Given that,

Mass of the quarterback, m = 80 kg

Mass of the football, m' = 0.43 kg

Speed of the football, v' = 15 m/s

We need to sort the following quantities as known or unknown.

1. The mass of the quarterback = known = 80 kg

2. The mass of the football = known = 0.43 kg

3. The horizontal velocity of quarterback before throwing the ball = known = 0

4. The horizontal velocity of football before being thrown = known = 0

5. The horizontal velocity of quarterback after throwing the ball, = unknown quantity and it can be calculated using the conservation of linear momentum.

6. The horizontal velocity of football after being thrown = known = 15 m/s

(a) The mass of the quarterback is known and equal to 80 kg

(b) The mass of the football is known and equal to 0.43 kg

(c) The horizontal velocity of quarterback before throwing the ball is known and equal to zero. The horizontal velocity of the quarterback before throwing the ball is zero as he jumps vertically upwards.

(d)The horizontal velocity of football before being thrown is known and is zero as the ball and quarterback have same initial velocity

(e) The horizontal velocity of quarterback after throwing the ball is an unknown quantity and by calculation, Speed of quarterback Vq = – 0.081m/s in the opposite direction as the ball.

(f) The horizontal velocity of football after being thrown = known = 15 m/s

Explanation:

Given mq = mass of quarterback = 80kg

mb = 0.43kg

Vb = 15m/s

Required to calculate the horizontal velocity of the quarterback = Vb

This problem involves the principle of conservation of momentum. By this principle the total sum of momentum before and after the quarterback throws the ball must be equal.

From the question there was no horizontal momentum before the ball was thrown. So the initial horizontal momentum of the quarterback and ball sum up to zero.

The final horizontal momentum is

0 = mbVb + mqVq

0 = 0.43×15 + 80Vq

80Vq = – 6.45

Vq = –6.45/80

Vq = – 0.081m/s in the opposite direction as the ball.

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