10) Haiya throws a 150.0 g axe at a 1.10 kg block of wood, with an initial velocity of 25.0 m/s [→]. The axe becomes stuck in the block of wood. The block of wood is attached to an overhead beam via a rope of length 2.30 m.
a) Calculate the velocity of the block of wood, with the axe stuck in it, after the collision.
b) After the collision, the block of wood will swing on its rope. Calculate the maximum height of the block.
c) Once the block reaches its maximum height, the rope makes an angle with its original vertical position. Calculate that angle.
11) A proton (m = 1.007 u) travels with a velocity of 2.33 !!! 10^6 m/s towards a Helium atom. The Helium atom (m = 4.0026 u) is travelling towards the proton with a velocity of 9.87 !!! 10^5 m/s. The head-on collision between these two particles is perfectly elastic in nature. [Recall: u represents the atomic mass unit, where: 1 u = 1.66 !!! 10^-27 kg]
a) Calculate the final velocity of each particle after the collision.
b) Demonstrate that kinetic energy was conserved in this scenario (i.e. show that the total kinetic energy in the system initially is equal to the total kinetic energy in the system after the collision).
12) Suppose a new variation of the game Billiards is invented. In this new variation, yellow balls have twice the mass of blue balls*. In one particular game session, a yellow ball is at rest, and a blue ball rolls towards it with a velocity of 4.95 m/s [W]. After the two balls collide, the blue ball ends up with a final velocity of 3.11 m/s [S8.43!!!W].
Determine the final velocity of the yellow ball.
*(Hint: this will help you to evaluate your mass ratios without needing to know the actual masses)