Motion in a Plane

Topics in this chapter

• Vector Algebra and Products
• Projectile Motion and Trajectories
• Relative Motion and River Crossings
• Circular Motion and Vertical Circles
• Two-Dimensional Kinematics

Cheat sheet

Practice questions

1. Question 1Q-35A2E8

   If the magnitude of the sum of two vectors is equal to the magnitude of their difference, what is the angle between the two vectors?

   1. A.$0^\circ$
   2. B.$45^\circ$
   3. C.$90^\circ$
   4. D.$180^\circ$
   See the answer and solution
2. Question 2Q-ACE6DB

   A particle moves in the xy-plane with a constant acceleration given by $\vec{a} = 3\hat{i} + 4\hat{j}\text{ m/s}^2$. At $t = 0$, the particle starts from the origin with an initial velocity $\vec{v}_0 = 2\hat{i}\text{ m/s}$. What is the magnitude of the particle's velocity at $t = 2\text{ s}$?

   1. A.$10\text{ m/s}$
   2. B.$5\sqrt{2}\text{ m/s}$
   3. C.$8\text{ m/s}$
   4. D.$6\sqrt{2}\text{ m/s}$
   See the answer and solution
3. Question 3Q-3D32A2

   A projectile is fired with an initial velocity $u$ at an angle $\theta$ with the horizontal. At what angle of projection is the horizontal range equal to four times the maximum height attained by the projectile?

   1. A.$30^\circ$
   2. B.$45^\circ$
   3. C.$60^\circ$
   4. D.$75^\circ$
   See the answer and solution
4. Question 4Q-6484B7

   Rain is falling vertically with a speed of $30\text{ m/s}$. A woman rides a bicycle with a speed of $10\sqrt{3}\text{ m/s}$ in the north to south direction. What is the apparent velocity and direction of rain with respect to the woman?

   1. A.$20\text{ m/s}$ at $30^\circ$ with vertical towards South
   2. B.$40\text{ m/s}$ at $60^\circ$ with vertical towards North
   3. C.$20\sqrt{3}\text{ m/s}$ at $60^\circ$ with vertical towards South
   4. D.$60\text{ m/s}$ at $30^\circ$ with vertical towards North
   See the answer and solution
5. Question 5Q-8D4C3E

   A particle is moving in a circle of radius $R$ with a constant speed $v$. What is the magnitude of the average acceleration during a time interval equal to half of the circular path?

   1. A.$\frac{v^2}{\pi R}$
   2. B.$\frac{2v^2}{\pi R}$
   3. C.$\frac{4v^2}{\pi R}$
   4. D.Zero
   See the answer and solution