16. Exercises

A car, of mass 1000 kg, is travelling at 20 \displaystyle \text{m}{{\text{s}}^{-1}}, when it drives into a truck, of mass 4000 kg, which was moving at 10 \displaystyle \text{m}{{\text{s}}^{-1}} in the same direction. After the collision the two vehicles move together. Find the speed of the vehicles after the collision.

A child of mass 40 kg stands on a skate board, of mass 2 kg. Initially both are at rest. The boy jumps off so that he travels horizontally at 3 \displaystyle \text{m}{{\text{s}}^{-1}}. Find the speed of the skateboard.

Two particles travel towards each other along a straight line. One has mass 3 kg and speed 4 \displaystyle \text{m}{{\text{s}}^{-1}}. The other has mass 5kg and speed 2 \displaystyle \text{m}{{\text{s}}^{-1}}. When they collide the 3kg mass is brought to rest. What happens to the 5kg mass ?

A toy train, of mass 200 grams, is moving along a straight track at 1.8 \displaystyle \text{m}{{\text{s}}^{-1}}, when it collides with a stationary truck of mass, of mass 300 grams, during the collision the truck is coupled to the train. Find the speed of the truck after the collision.

Two particles are travelling towards each other when they collide. One has mass 2kg and was travelling at 5 \displaystyle \text{m}{{\text{s}}^{-1}} before the collision and the other has mass 3 kg and a velocity of 6 \displaystyle \text{m}{{\text{s}}^{-1}} before the collision. The 2kg mass changes direction and moves at 2 \displaystyle \text{m}{{\text{s}}^{-1}} after the collision. Describe how the 3kg mass moves after the collision.

Two particles A and B, have masses 2 kg and 3kg respectively. Before a collision between the two particles, they have velocities (\displaystyle 9\mathbf{i}+5\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} and (\displaystyle -3\mathbf{i}+4\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} respectively, where \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are perpendicular unit vectors. During the collision the two particles coalesce and move together after the collision.

Find the velocity of the particles after the collision.

Two identical particles, A and B are travelling in perpendicular directions when they collide. Particle A is travelling at 5 \displaystyle \text{m}{{\text{s}}^{-1}} and B at 8 \displaystyle \text{m}{{\text{s}}^{-1}} when they collide. During the collision the particles coalesce to form a single particle.

a) Find the speed of the combined particle after the collision.

b) Find the angle between the velocity of A before the collision and the velocity of the combined particle after the collision.

Red and white snooker balls have the same mass. A white ball is moving at 1 \displaystyle \text{m}{{\text{s}}^{-1}}, when it collides with a red ball which is at rest. After the collision the white ball travels at 0.8 \displaystyle \text{m}{{\text{s}}^{-1}} and it is deflected through 60\displaystyle {}^\circ from its original path. Find the speed of the red ball after the collision.

Two particles, A and B, have velocities (\displaystyle 8\mathbf{i}+7\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} and \displaystyle U\mathbf{i}+V\mathbf{j} respectively when they collide. After the collision A travels in the direction of \displaystyle \mathbf{i} at 5 \displaystyle \text{m}{{\text{s}}^{-1}} and B travels in the direction of \displaystyle \mathbf{j} at 2 \displaystyle \text{m}{{\text{s}}^{-1}}. Given that the mass of A is twice the mass of B, find U and V.

Two particles, A and B, have velocities (\displaystyle 5\mathbf{i}+V\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} and (\displaystyle 2\mathbf{i}-V\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} respectively. The mass of A is m and the mass of B is \displaystyle \lambda m. After the collision, the particles move together with velocity (\displaystyle 3\mathbf{i}-2\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}}.

a) Find \displaystyle \lambda .

b) Find V.