You throw a firecracker vertically upward. At \(t = 0\text{,}\) the firecracker is moving upward with speed \(v_1\text{,}\) at which point it begins to explode, splitting into an upper piece with mass \(m_u\) and a lower piece with mass \(m_l\text{.}\) The explosion finishes at \(t = \frac{v_1}{g}\text{,}\) at which point you observe that the upper piece is still moving upward with speed \(3v_1\text{.}\)
A \(70 \mathrm{~kg}\) soccer player, running at \(10 \mathrm{~m/s}\text{,}\) kicks a \(0.4 \mathrm{~kg}\) ball, which then travels at \(50 \mathrm{~m/s}\text{.}\) What is the magnitude of the player’s linear momentum? What is the magnitude of the ball’s linear momentum?
The ball from the previous problem is then kicked back towards the player, so that it is now traveling in the opposite direction with the same speed. Has the linear momentum of the ball changed? When the ball was kicked back towards the player, if the foot was in contact with the ball for \(0.22 \mathrm{~s}\text{,}\) what was the magnitude of the impulse that acted on the ball?
A force \(F\) pushes a car with a small mass \(m\text{.}\) Another, identical force \(F\) pushes a truck with a bigger mass \(M\text{.}\) The car and truck are both pushed for the same amount of time. Is the car or the truck going faster at the end of the time?
A \(50 \mathrm{~g}\) ball of clay traveling at speed \(v_0\) hits and sticks to a \(1.0 \mathrm{~kg}\) brick sitting at rest on a frictionless surface. What is the speed of the brick after the collision?
