Gerry, the gerbil, walks 55 cm in the positive y-direction. After this, he is located 95 cm from the origin at an angle of 50 degrees from the positive x-axis towards the positive y-axis, as shown in the figure.

1. Complete the figure by including the change in position and the initial position vectors.

2. Calculate Gerry’s initial position.  

Deserted on a deserted Island, you spot a slightly exposed tin can under a tree. Upon opening it, you find it is instructions to a treasure. It reads:

1. Ten paces from this very tree, in a direction twenty degrees south of west, lies the first location. 

2. Ten paces from this very tree, in a direction sixty degrees north of east, lies the second location. 

3. Walk from this tree exactly the distance and direction you would walk from the first location to the second location, and you will find a treasure. Yar! 

Find the coordinates of the treasure. 

An amusement park roller coaster starts out on a level track 5 m long and then goes up a 25 m incline at an angle of 30° up from the horizontal. Finally, it goes down a 15 m ramp with an incline of 40° below the horizontal. Consider the entire trip to when the coaster has reached the final ramp’s bottom. Assume it takes one minute to reach the end of the last ramp. 

1. What is the total distance traveled?

2. What is its displacement from its starting point?

3. What is the distance from the starting point?

4. What is the average speed during the trip?

5. What is the average velocity during the trip?

During the middle of a family picnic, Barry Allen received a message that their friends, Bruce and Hal, needed to be saved. Barry promised his partner, Iris, he would return in exactly 5 minutes. From that picnic location, Barry runs at a speed of 600 m/s  for 2 minutes at a heading of 35° north of west to save Bruce. He then changed his heading to 30° west of north but slows down to 400 m/s   and runs for 1 minute to save Hal. (The speed changes are essentially instantaneous and not part of solving this problem). 

1. Draw a physical representation of the displacement during Barry’s entire trip.

2. What average velocity (magnitude and direction) does Barry need to return to the picnic to keep his promise to Iris? 

The figure shows a plot of a car’s velocity as a function of time. 

1. 1. 1. Find the car’s acceleration at times t=3 [s], at t=7 [s], and at t=11 [s]. 

      2. How far does the car travel between t=2 [s]  and t=13 [s]? 

      3. Sketch a plot of the car’s position as a function of time. Appropriately scale and number the axes. 

      4. Sketch a plot of the car’s acceleration as a function of time. Appropriately scale and number the axes. 

Two objects start from the same location and time but have different accelerations and initial velocities. We are asked to calculate the final location they meet again, and the time this process takes. In addition, we need to sketch the position vs. time (x-t) plot of the objects. 

Two objects, one with a contact speed, the other one with a constant speed race. First, we are asked to work on a 1D kinematic problem; then, we take the final values of part (a) and use them as the initial values of part (b). In part (b), we work on a complex projectile motion with a contact acceleration along the x and y-axis.