It’s a beautiful winter day, and you and your friend are throwing around a 5 kg medicine ball on a very slippery frozen lake. You throw the ball toward your friend, and notice that you subsequently slide backwards with a speed of 1 m/s. If your mass is 60 kg, how fast did you throw the ball?
To find the speed at which you threw the ball, we can apply the principle of conservation of momentum. The total momentum before and after the throw should be equal.
First, let's calculate the momentum before the throw. Since you are sliding backward with a speed of 1 m/s, your momentum can be calculated as:
Momentum_before = mass * velocity = 60 kg * (-1 m/s) = -60 kg·m/s
Here, the negative sign is used because the momentum is in the opposite direction of your movement.
Next, let's calculate the momentum after the throw. The momentum of the ball can be calculated using the same formula:
Momentum_after = mass * velocity
Let's denote the velocity at which you threw the ball as v. Since the mass of the ball is 5 kg, the momentum of the ball after the throw would be:
Momentum_of_ball = 5 kg * v
Since the total momentum before and after the throw must be equal, we can set up an equation:
-60 kg·m/s = 5 kg * v
Now, we can solve for v:
v = (-60 kg·m/s) / (5 kg) = -12 m/s
Therefore, you threw the ball with a speed of -12 m/s. The negative sign indicates that the ball was thrown in the opposite direction of your movement.