PHYS 313 Test 1. Box your answers. Submit a scanned pdf on 8 1/2 “ by 11” letter paper, or submit an
electronic version having used a stylus. Do not submit notebook paper or work that is not neatly
handwritten.
You are leaving campus driving north on Hillside, and you turn onto 21st street from Hillside traveling
east at a constant velocity of vx = 40 mph (or 2/3 miles/minute). Halfway between Hillside and Oliver
Ave. (about ½ mile you hit a red light at the crossing for the fraternities and sororities.) 30 seconds later
the light turns green. Continuing at the same 40mph you cross Oliver Ave with a green light and
continue to Woodlawn where you get another red light for another minute. Once the light turns green
you continue east at 40 mph until you are halfway between Woodlawn and Rock Rd. You then enter a
construction zone limiting your speed to 20 mph. You a
ive at your destination of 21st and Rock Rd. for
a quick lunch and some grocery shopping at Dillon’s.
a. Draw an accurate position vs. time graph for your drive from 21st and Hillside (at time t = 0 min)
to 21st and Rock. Use a numerical scale of minutes for time and miles for position. Label each
coordinate (t, x) where the shape of the graph changes. Assume that the time to accelerate to
different velocities is negligible.
. Directly below the graph from part a) draw an accurate velocity vs. time graph of your motion
during the trip. Use minutes for the times axis and mph for the vertical velocity axis (I know,
lopes would be in uits of mies/(hr*min) but you shouldn’t have any slopes in your graph.) Place
the time axis of the graph directly under the time axis of the position graph so an imaginary
vertical line can pass through equal times on each graph. Again, assume the time to accelerate
to different velocities is negligible.
You may just want to draw these on another sheet of paper.
2. Throwing a tennis ball in the air when you’re bored is always fun. Now that you are in physics, it’s a
equirement of the syllabus that you think about the motion while you’re doing this. Suppose you are
holding the tennis ball 0.50 m above the floor. During the throw your hand moves upward by 1.0 m.
Once the ball has left contact with your hand it travels another 1.5m. After reaching its highest point in
then falls 3.0 m back to and impacts the ground. Assume the motion is vertical, and ignore drag.
a. Draw an appropriate pictorial representation of the ball as in the textbook. Include all important
instances (start of throw, ball leaving hand, reaching max height, impacting ground) with 0,1,2, and 3.
List all known quantities.
. For the throw, determine the launch velocity (v1, the acceleration of the throw, and the time the ball was in contact
with your hand.
c. Draw position, velocity, and acceleration graphs for the entirety of the throw until the ball impacts
the ground. Graph x vs. t on top, v vs. t blow position, and a vs. t at the bottom. Be sure to align the time
axes. Include appropriate numerical scales.
3. Projectile Motion. Consider the range equation XXXXXXXXXXgiven in the textbook for a projectile launched
with initial velocity v0 and angle θ that returns to its initial launch height (for instance, on a flat, level
desert.) The height H of this projectile is given by
H = v02 sin
2
θ / (2g)
You can verify this, if you want.
a. Invert those two equations to solve for launch angle θ(H, R) in terms of H and R.
. Using the result for part a, solve for the launch velocity v0(H, R) in terms of H and R.