Ten sense-making tasks on motion in one and two dimensions. Explain your reasoning for every answer. The explanation counts as much as the answer.
showmethephysics.com
Six balls are launched from level ground with the speeds and angles shown. Ignore air resistance. Each ball lands back on the same level ground.
Rank the balls by their time in the air, from longest to shortest. If any are equal, show the tie. If the ranking cannot be determined, say so.
Longest 1 ____ 2 ____ 3 ____ 4 ____ 5 ____ 6 ____ Shortest
Explain your reasoning.
Back to topBall A is dropped from the top of a 20 m cliff. At the same instant, an identical Ball B is thrown horizontally at 15 m/s from an identical 20 m cliff. Ignore air resistance. Three students argue about which ball hits the ground first.
Ava: "Ball A lands first. Ball B has to travel a longer path, so it takes more time."
Ben: "Ball B lands first. It's moving faster the whole time, so it gets there sooner."
Cam: "They land at the same time. The horizontal motion doesn't change how fast each ball falls."
Which student(s), if any, do you agree with? Explain what is right or wrong about each statement. Then find the time each ball takes to land.
Back to topA soccer ball is kicked from level ground and follows the dashed path. Ignore air resistance. A student draws the ball's velocity vector at five points. At the top (point R), the student writes "v = 0" because "the ball stops going up."
What, if anything, is wrong with the student's diagram? If something is wrong, explain the error and describe the correct vector(s). If nothing is wrong, explain why it is correct.
Back to topA cart moves along a straight horizontal track. To the right is the positive direction. For each situation, choose the sign of the cart's acceleration:
A. positive B. negative C. zero D. cannot be determined
| Situation | Choice |
|---|---|
| (a) Moving right and speeding up | |
| (b) Moving right and slowing down | |
| (c) Moving left and speeding up | |
| (d) Moving left and slowing down | |
| (e) Moving left at a constant 3 m/s | |
| (f) Rolled up a ramp that rises to the right, momentarily at rest at its highest point | |
| (g) At rest at one instant (no other information) |
Explain the rule you used. Does "negative acceleration" always mean "slowing down"?
Back to topFrom the edge of a 25 m tall roof, Ball 1 is thrown straight up at 20 m/s and an identical Ball 2 is thrown straight down at 20 m/s. Ignore air resistance.
For each quantity, state whether it is greater for Ball 1, greater for Ball 2, the same for both, or cannot be determined.
| Quantity | Answer |
|---|---|
| (a) Acceleration halfway through each ball's flight | |
| (b) Time from release until hitting the ground | |
| (c) Displacement from release until hitting the ground | |
| (d) Speed just before hitting the ground |
Explain each answer. Then check (b) and (d) with numbers, using $g = 10\ \text{m/s}^2$.
Back to topA cart rolls to the right at a constant 3.0 m/s. A spring launcher on the cart fires a ball straight up (relative to the cart) at 5.0 m/s. Ignore air resistance.
The two equations below describe the motion of one object in some physical situation:
$$-45\ \text{m} = (0\ \text{m/s})\,t - \tfrac{1}{2}(10\ \text{m/s}^2)\,t^2$$
$$\Delta x = (12\ \text{m/s})\,t$$
The graph shows the position of a toy car moving along a straight hallway.
A soccer ball is kicked from level ground at 25 m/s, 37° above the horizontal. Find how far away it lands. Use $g = 10\ \text{m/s}^2$, $\sin37^\circ = 0.60$, $\cos37^\circ = 0.80$. Ignore air resistance.
Student solution:
$v_x = (25\ \text{m/s})\cos37^\circ = 20\ \text{m/s}$
Time to reach the top: $0 = 25\ \text{m/s} - (10\ \text{m/s}^2)t \Rightarrow t = 2.5\ \text{s}$
Total time in air: $2(2.5\ \text{s}) = 5.0\ \text{s}$
Range: $\Delta x = (20\ \text{m/s})(5.0\ \text{s}) = 100\ \text{m}$
Identify the error in the solution. Explain the physics of why it's an error, then find the correct range.
Back to topA driver goes from home to a store 30 km east at a steady 60 km/h. On the way back (30 km west), traffic is heavy and she drives at a steady 30 km/h.
Riley writes: "Her average velocity for the whole trip is $\dfrac{60\ \text{km/h} + 30\ \text{km/h}}{2} = 45\ \text{km/h}$."