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.

*Q2.1) You’ve been driving down the freeway due East for 45 minutes at 110 km/hr when you suddenly realize that you’ve missed your exit. You pull a U-turn and head due West at 120 km/hr for 5 minutes before finally exiting the freeway and proceeding to drive due North at 80 km/hr for 30 minutes towards your destination. Ignore any distance travelled while accelerating.

a) What was the total distance travelled during the entire trip?

b) What was the total displacement over the course of the entire trip?

c) What was the average speed over course of the entire trip?

d) What was the average velocity over course of the entire trip?

**Q2.2) In frustration, you hurl your physics textbook with an initial velocity of 25m/s at an angle of 30 degrees above the ground. Your friend, recognizing that textbooks are expensive, runs some distance and catches the book at the same height from which it was thrown.

a) What’s the speed of the book when it’s at its maximum height?

b) What’s the speed of the book when it strikes your friend?

c) What’s the maximum height reached by the book?

d) How far away from you is your friend at the moment he catches the book?

**Q2.3) You open instagram one day to see a video of Ellen deGeneres complaining about quarantine from the comfort of her $40 million Belair mansion. You decide to toss your phone off a cliff. If you toss the phone with an initial velocity of 15m/s at an angle of 40 degrees above the horizontal, what’s the velocity of the phone when it strikes the ground 20m below?

**Q2.4) A gazelle is casually jaunting Eastward at a constant 5m/s for 2 minutes before spotting a cheetah in the bushes. In a panic, the gazelle turns to the direction 15 degrees East of South and accelerates at a rate of 1.8m/s² for 14 seconds. What’s the total displacement of the gazelle?

***Q2.5) You and your friend are in an airplane travelling at a velocity of 80m/s horizontally, at an altitude of 2000m from the ground. Eager for his first skydiving experience, your friend drops out of the plane. Realizing that he forgot his parachute, you jump out of the plane 1.2 seconds later, pushing off the plane with an initial velocity of 12.5m/s downward (relative to the airplane). Do you catch your friend before he hits the ground? If so, through what vertical distance do you fall before catching him? Ignore air resistance.

*Q2.6) You’re on a train that is travelling with a velocity of 45m/s North. You get out of your seat and walk towards the back of the train with a speed of 1.5m/s.

a) What is your velocity according to an observer that is sat in their seat on the train?

b) What is your velocity according to an observer that is stationary on the ground outside the train, watching with binoculars through the window?

**Q2.7) An observer on the shore watches you paddle straight East across a river in 8 seconds. If the river was 12m wide and flowing straight North at 3m/s, what must have been your velocity relative to the water?

***Q2.8) A plane wants to fly from Toronto to guelph in 30 minutes. If the city of Guelph is located 60km from Toronto in the direction 15 degrees South of West, and there is wind blowing at 40km/hr in the direction 30 degrees North of West, in what direction and with what speed must the plane fly to make the trip in exactly 30 minutes? Hint: Start by drawing the vector diagram that includes the wind velocity, the plane’s air velocity, and the plane’s ground velocity.