Exam 3: Vectors and Motion in Two Dimensions

You are driving at $30.0 \mathrm {~m} / \mathrm { s }$ on a freeway curve of radius $25.0 \mathrm {~m}$ What is the magnitude of your acceleration?

A projectile is fired from the edge of a cliff as shown in the figure. The initial velocity components are 940 m/s (horizontal)and 96 m/s (vertical). The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. How high is point P above point Q, assuming no air resistance?

A pickup truck moves at 25 m/s toward the east. Ahmed is standing in the back and throws a baseball in what to him is the southwest direction at 28 m/s (with respect to the truck). A person at rest on the ground would see the ball moving how fast in what direction?

A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal. If air resistance is negligible, how high above the projection point is the ball after 2.0 s?

A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which of the following statements about the rock's motion are true just before it hits the ground? (There could be more than one correct choice.)

If $\overrightarrow { \mathrm { A } }$ - $\overrightarrow { \mathrm { B } }$ = 0, then the vectors $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ have equal magnitudes and are directed in the same direction.

A girl throws a rock horizontally with a speed of 12 m/s from a bridge. It falls 2.28 s before hitting the water below. Neglect air resistance. (a)How high is the bridge from the water below? (b)How far horizontally does the rock travel before striking the water?

Vector $\overrightarrow { \mathrm { A } }$ has a magnitude of 6.0 m and points 30° north of east. Vector $\overrightarrow { \mathrm { B } }$ has a magnitude of 4.0 m and points 30° west of south. The resultant vector $\overrightarrow { \mathrm { A } }$ + $\overrightarrow { \mathrm { B } }$ is given by

Two boys, Joe and Sam, who are searching for buried treasure start underneath the same tree. Joe walks 12 m east and then 12 m north, while Sam walks 15 m west and then 10 m south. Both boys then stop. Find the magnitude and direction of the vector from Sam to Joe. Express the direction of this vector by specifying the angle it makes with the west-to-east direction.

The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively. If there is no air resistance, how long does it take the football to reach the top of its trajectory?

Vector $\overrightarrow { \mathrm { A } }$ has magnitude 2 units and is directed to the north. Vector $\overrightarrow { \mathrm { B } }$ has magnitude $5 \text { units }$ and is directed to the south. Calculate the magnitude and direction of $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } }$

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. If we neglect air resistance, the magnitude of the acceleration of the ball while it is in flight is

A projectile is fired from ground level with a speed of 150 m/s at an angle 30° above the horizontal on an airless planet where g = 10.0 m/s². What is the horizontal component of its velocity after 4.0 s?

The components of vectors $\overrightarrow { \mathrm { B } }$ and $\overrightarrow { \mathrm { C } }$ are given as follows: $B _ { x }$ = -9.2 $C _ { x }$ = -4.5 $B _ { y }$ = -6.1 $C _ { y }$ = 4.3 The angle (less than 180°)between vectors $\overrightarrow { \mathrm { B } }$ and $\overrightarrow { \mathrm { C } }$ is closest to

As shown in the figure, a heavy rock is shot upward from the edge of a vertical cliff. It leaves the edge of the cliff with an initial velocity of 15 m/s directed at 25° from the vertical and experiences no appreciable air resistance as it travels. How high is the cliff?

A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?

If $\overrightarrow { \mathrm { A } }$ + $\overrightarrow { \mathrm { B } }$ = $\overrightarrow { \mathrm { C } }$ and their magnitudes are given by A + B = C, then the vectors $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ are oriented

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. How fast can she swim in still water?

Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the following statements are true about just as the snowballs reach the ground below? (There could be more than one correct choice.)

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of the circular section of a dive. What is the radius of curvature of this section of the dive?