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.

*Q1.1) Consider the following three vectors. Roughly sketch the resultant vector R if:

a) R = A + B + C

b) R = A + B - C

c) R = A - B - C

*Q1.2) Find the x and y components of the vectors A , B, and C from Q1.1.

**Q1.3) Find the magnitude and direction of each of the resultant vectors from Q1.1. Do your results agree with your sketches?

*Q1.4) A car drives down the freeway at a constant velocity of 35m/s. How far does it travel in 1.5 hours?

*Q1.5) The car from Q1.4 exits the freeway and brakes for 8 seconds, causing it to slow down at a rate of 2 m/s². How far does the car travel while braking?

**Q1.6) You’re driving down a highway at a constant 100km/hr when suddenly a deer appears on the road, 65m in front of your car. If it takes 0.5 seconds for you to react and start braking, and your car can decelerate at a rate of 8m/s², do you hit the deer? If not, how far away are you from the deer by the time your car comes to a stop?

**Q1.7) You throw a ball with an initial velocity of 15 m/s straight upward.

a) What will be its velocity when it reaches maximum height?

b) Assuming you havn’t moved your hand, what will be the velocity of the ball when you catch it?

c) If you threw the ball from an initial height of 1.5 meters from the ground, what will be the maximum height reached by the ball?

**Q1.8) Your friend is standing 3.5m above you on the roof of your house and needs to do some emergency calculating. He asks you to toss him your calculator, so you toss it straight upward with an initial speed of 22m/s. Startled by the impressive speed of your throw, he misses the calculator on its way up, but manages to catch it on its way back down. How long is the calculator in the air?

***Q1.9) You’re sitting in your backyard relaxing on a calm Saturday afternoon, when suddenly your friend runs by at a constant 8m/s and smacks you in the back of the head as he passes. Startled, you get up and begin accelerating from rest at 1.5m/s² in chase.

a) How much time passes before you catch up to your friend?

b) How far do you run in the process of catching up to your friend?

c) How fast are you going by the time you catch up? Is this realistic?

***Q1.10) You and your friend are standing in front of a well. You don’t know how deep the well is, but you know that there’s plenty of water at the bottom. Like the keen young scientist that you are, you pull out your stopwatch and push your friend into the well. Precisely 2.4 seconds pass before you hear the sound of your friend splashing into the water at the bottom. Calculate the depth of the well, given that the speed of sound in air is 343 m/s. Hint: don’t forget to account for the time it takes for the sound to travel from the bottom of the well up to your ears.

***Q1.11) Usain Bolt famously set the men’s 100m sprinting record in 2009, with an astonishing time of 9.58 seconds. He reached his maximum speed after the first 4.5 seconds and continued at top-speed for the remainder of the race. Assuming constant acceleration,

a) Find Usain’s top speed.

b) Find Usain’s acceleration during the first 4.5 seconds of the race. How does this compare to gravitational acceleration on the surface of Earth?