Chapter 3: Two-Dimensional Motion and Vectors
Please answer questions in complete sentences, indicating the question asked and justifying the answer when necessary. Show work on problems, including the equation(s) used. Include significant figures and units in your boxed answer.
Leave a space between each question (or problem).
Section 3-1
Do Section Review #1-4 on page 87. You are to use graphical techniques (pencil, ruler, and protractor).
1. Is speed a vector or a scalar quantity? What about velocity? Explain.
2. What is the name of the vector that is made from two or more vectors that are added?
3. What is the maximum possible resultant of two vectors with magnitudes 4 and 5 units? What is the minimum possible resultant?
4. Do vectors have to be added in a particular order? Draw a diagram to support your answer.
5. How do you subtract a vector? Draw a diagram to support your answer.
Section 3-2
6. If you swim in a direction directly across a river and you end up downstream due to the flow of the water, do you move faster than you would if the water didn’t flow? Explain.
7. What do you call the process of determining the components of a vector?
8. A plane heading due north at 125 m/s is blown west at 25.0 m/s by a very strong wind. What is the plane's resultant speed and direction? 127 m/s @ 11.3o
9. A car travels 32.5 km south, then turns west and travels another 24.3 km. The car then turns to the north and goes 11.9 km. What distance does the car travel? What is the car's displacement? 68.7 km; 31.9 km @229.7o (49.7o west of south)
10. A motorboat travels at 8.5 m/s. It heads straight across a river that is 110 m wide. If the water flows at a rate of 3.8 m/s, what is the boat's resultant speed? How much time does it take for the boat to reach the opposite shore? How far downstream is the boat when it reaches the other shore? 9.3 m/s, 13 s, 49 m
11. A rocket is launched at a 32o angle (above the horizontal) with a speed of 450 m/s. What are the horizontal and vertical components of the rocket’s velocity? 380 m/s, 240 m/s
12. A football is punted at a 59o angle (above the horizontal) at 18 m/s. What is the horizontal speed of the football? How far will the ball travel horizontally if it remains in the air for 4.2 seconds? 9.3 m/s, 39 m
13. An airplane is traveling north-east on a 47.0o bearing. What is the eastward component of its velocity if the northward component is 312 km/hr? 335 km/hr
Section 3-3
14. In the absence of air resistance, why does the horizontal component of velocity for a projectile remain constant even though the vertical component changes?
15. Ignoring air resistance, which will hit the ground first: a dropped ball or a horizontally-projected ball if they begin at the same height? Explain.
16. A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? Its horizontal acceleration?
17. At what angle should a projectile be fired for maximum altitude? For maximum range?
18. In the presence of air resistance, does a projectile follow a parabolic path? Explain.
19. A rock is thrown horizontally at a speed of 6.5 m/s from the top of a 55 m high cliff. How long does it take to hit the ground? 3.3 s
20. How far from the base of the cliff does the rock in the previous problem land? 22 m
21. What would be the range if the rock is thrown with twice the horizontal velocity? 43 m
22. A ball rolls with a constant horizontal velocity on a tabletop 0.855 m high. If the ball rolls off and hits the ground 0.345 m from the edge of the table, how fast was the ball rolling? 0.827 m/s
23. A ball moving at 2.45 m/s rolls off a table and hits the ground 1.55 m from the edge. How high is the table? 1.96 m
24. A golf ball is hit with a velocity of 28.9 m/s at an angle of 35.0o above the horizontal. What is the “hang time” of the ball? In other words, for how much time is the ball in the air before it hits the ground? 3.38 s
25. What is the range (x-displacement) of the ball in the previous question? 80 m (8.0 x 101 m)
26. What is the maximum height of the ball in the previous problem? Hint: how much time does it take for the ball to fall from its maximum height to the ground? 14 m
27. A place kicker attempts a 36.0 m field goal by kicking the ball at a 53.0o angle at 20.0 m/s. If the crossbar is 3.05 m high, by how much does the football clear or fall short of the crossbar? The ball clears the crossbar by about 0.85 m.