General Physics with Calculus
1. Problem 1: Directions to Class
Figure 1: Campus map with legend for distance measurements and three locations (W), (VL), and(RS)
(a) Use the campus map above to map your way from the bus stop at the Stadium to
Library for a snack.
Draw the vectors that you would walk to reach your destination and assign an appropriate direction and magnitude to each one. And no cutting through buildings.
Don’t forget your axes, vector labels, and to use basis vectors for your directions: ˆx and ˆy.
(b) After getting a snack map your way from Library to Hall for lecture.
(c) Calculate the total length of your walk.
(d) If if took you 15 minutes to walk the whole path (not counting your time in the library), what
was your average speed?
(e) Sensemaking: How does you average speed compare to the average speed of a person walking
around town (1.4m/s)?
2. Problem 2: Kinematics on an Inclined Plane (Adapted form Knight)
A bowling ball rolls along a level surface, then up a 30◦
slope, and finally exits onto another level
surface at a slower speed as.
Figure 2: The bowling ball’s initial conditions.
(a) Draw position-versus-time, velocity-versus-time, and acceleration-versus-time graphs for the ball.
Don’t forget your coordinate system and to mark important point (where do things change?) on
For the rest of the problem suppose that the balls initial speed is 5m/s and it’s final speed is 1m/s.
(b) List all knowns and unknowns. For all values you should have symbol = number or symbol =?.
Don’t forget to include our units.
(c) Sensemaking: Draw a pictorial representation that you would use to determine the height h of
the slope. Don’t forget your coordinate system.
Hint: Rotate your coordinate system.
(d) Solve for the length l of the incline using 1-dimensional kinematics. For this part do not plug in
any numerical values, give a completely symbolic answer.
(e) Solve for the numerical value of l
(f) Solve for the height h of the incline using trigonometry For this part do not plug in any numerical
values, give a completely symbolic answer.
(g) Solve for the numerical value of h
(h) Sensemaking: Check your units for part (e)
(i) Sensemaking: What would you expect the height to be if the incline was horizontal (θ = 0◦
the incline was vertical (θ = 90◦
)? Does your equation from part (g) match your intuitions?
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.