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# Motion in Two Dimensions Practice Questions

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Review these concepts at: Motion in Two Dimensions Study Guide

## Practice Questions

1. In your daily travels, you leave home in the morning, go to school and then to volleyball practice, and return home 8 hours later. During this entire trip, compare the distance and the displacement.
2. During a board game, you move a piece first 10 cm toward the east and then 8 cm toward the northeast. Find the total displacement of the piece as a vector.
3. In the previous practice problem, compare displacement with the distance traveled by the piece.
4. When the speed of an object is constant, does that mean that its velocity is constant also?
5. Show on a diagram the displacement of a car that moves between the following positions: (20,20) meters to (60,50) meters in 2.5 seconds, and then calculate displacement and the average velocity, both expressed with their coordinates and magnitude and angle.
6. Consider a rock held by a string and rotated in a circle. Choosing two positions on the trajectory, draw the instantaneous velocity at those points and then draw the average acceleration.
7. An airplane travels with a velocity of 34 m/s relative to air due north, and the wind blows at 7 m/s due north. What is the relative velocity of the airplane relative to Earth?
1. A boat's engine develops a velocity of 11.0 m/s when the boat is moving across the river and the water current is 2.00 m/s downstream. Find the relative speed of the boat with respect to an observer on the shore.
2. A drop of rain moves downward at a velocity of 5 m/s and hits a car window that moves due east at 28 m/s. Find the angle of the mark the raindrop leaves on the window.
1. At the top of the trajectory, is the velocity of the object moving in a projectile motion equal to zero or nonzero? Describe.
2. A rock is thrown with an initial speed and at an angle with respect to the horizontal. At what time is the acceleration zero?
3. Find the range and the maximum height if a rock is thrown with an initial velocity of 10.0 m/s first at an angle of 20.0° and then at an angle of 45.0°.

1. Although displacement is zero, since the person returns to the same place where the motion started from, distance is not zero.
2. The resultant is (15.7,5.7) cm or 16.7 cm and 20° north of east.
3. The distance is 18 cm, while displacement is 16.7 cm.
4. No, although the magnitude might stay constant, as in the case of a car, the object might move on a curve and then, due to the change in direction, velocity changes, too.
5. Displacement is (40,30) m or 50 m and 37° north of east. Average velocity is (16,12) m/s or 20 m/s at 37° north of east.
6. I will choose two far away points for clarity:
7. vr = 41 m/s due north
8. vr = 11.2 m/s at 10.3° downward
9. 80° west of south (if we consider downward direction south)
10. It's nonzero since on the x-axis, the object moves with constant velocity all the time.
11. At no time, because the acceleration due to gravity is constantly nonzero
12. R = 10.2 m and h = 2.55 m

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