Note: problem difficulty is ranked using a star system.

• (*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.

• (**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.

• (***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.

*Q5.1) A fully-loaded semi truck has a mass of about 40 000 kg. If such a truck is travelling in the direction 40 degrees West of North and covers 450km in 3 hours, what’s its momentum in SI units?

*Q5.2) A Tesla Model 3 has a mass of about 1600kg. If such a Tesla is travelling 35m/s in the direction 40 degrees East of South collides head-on with the semi truck from Q5.1 and sticks to it, what will be the velocity of the wreckage immediately after the collision?

*Q5.3) You fire a 250g arrow with a velocity of 86m/s perfectly horizontally towards a stationary wooden block of mass 20kg. If the arrow sticks in the block, with what velocity will the arrow and block move after the collision?

**Q5.4) An astronaut is on a space-walk to do some repairs on the International Space Station (ISS), when suddenly she detaches from her tether and begins drifting away from the ISS at 30 cm/s (relative to the ISS). As a last-ditch effort to save herself, she removes the glove of her space-suit and throws it with a velocity of 15 m/s in the direction of her drift. Is this enough to save her? What’s her velocity relative to the ISS after she throws her glove? Assume the mass of the astronaut while fully suited is 80kg, and the mass of her glove is 2kg.

**Q5.5) Show that conservation of momentum follows directly from Newton’s laws. Hint: consider the impulses acting on two objects that have collided with one another.

**Q5.6) Consider a spherical cow of mass 700kg rolling Eastward at 8m/s. Imagine that you want to change the velocity of this cow by bowling a spherical chicken of mass 4kg towards the cow, resulting in a collision. With what velocity must you bowl the chicken so that, after the collision, the cow is rolling Northward at 2m/s and the chicken is stationary?

**Q5.7) Two billiard balls of equal mass (1 kg) collide as shown below.

a) Find the velocity of the red ball after the collision.

b) Check whether this collision is elastic or inelastic.

**Q5.8) A 5kg box is released from rest and let slide down the frictionless ramp shown below. When it reaches the bottom of the ramp, it collides with and sticks to a stationary 10kg box. Find the velocity of the two boxes after the collision.

***Q5.9) A firework is launched perfectly upward with an initial velocity of 220 m/s.When it reaches a height of 1500 m from the ground, it explodes into three pieces of equal mass with velocities shown below. With what speed will piece 3 strike the ground? Ignore air resistance and assume that the firework has no on-board means of propulsion.