By Valentina Tobos | Laurentiu Tobos

Updated on Sep 26, 2011

Review these concepts at: Motion in Two Dimensions Study Guide

**Practice Questions**

- 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.
- 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.
- In the previous practice problem, compare displacement with the distance traveled by the piece.
- When the speed of an object is constant, does that mean that its velocity is constant also?
- 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.
- 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.
- 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?

- 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.
- 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.

- At the top of the trajectory, is the velocity of the object moving in a projectile motion equal to zero or nonzero? Describe.
- A rock is thrown with an initial speed and at an angle with respect to the horizontal. At what time is the acceleration zero?
- 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°.

**Answers**

- Although displacement is zero, since the person returns to the same place where the motion started from, distance is not zero.
- The resultant is (15.7,5.7) cm or 16.7 cm and 20° north of east.
- The distance is 18 cm, while displacement is 16.7 cm.
- 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.
- 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.
- I will choose two far away points for clarity:
*v*= 41 m/s due north_{r}*v*= 11.2 m/s at 10.3° downward_{r}- 80° west of south (if we consider downward direction south)
- It's nonzero since on the
*x*-axis, the object moves with constant velocity all the time. - At no time, because the acceleration due to gravity is constantly nonzero
*R*= 10.2 m and*h*= 2.55 m

From Physics Success in 20 Minutes A Day. Copyright © 2006 by LearningExpress, LLC. All Rights Reserved.

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