Exam 3: Vectors and Motion in Two Dimensions

Refer to the figure, which shows four vectors $\overrightarrow { \mathrm { M } }$ , $\vec { N }$ $\overrightarrow { \mathrm { s } }$ , and $\vec { T }$ . (a) Vector $\overrightarrow { \mathrm { s } }$ as expressed in terms of vectors $\overrightarrow { \mathbf { M } }$ and $\vec { N }$ is given by A) $\overrightarrow { \mathrm { M } }$ + $\overrightarrow { \mathrm { N } }$ . B) $\overrightarrow { \mathrm { M } }$ - $\overrightarrow { \mathrm { N } }$ . C) $\vec { N }$ - $\overrightarrow { \mathbf { M } }$ . (b) Vector $\overrightarrow { \mathrm { T } }$ as expressed in terms of vectors $\overrightarrow { \mathrm { M } }$ and $\overrightarrow { \mathrm { N } }$ and is given by A) $\vec { N }$ + $\overrightarrow { \mathrm { M } }$ B) $\overrightarrow { \mathrm { M } }$ - $\vec { N }$ C) $\vec { N }$ - $\vec { M }$

A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s². The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what angle was the projectile fired above the horizontal?

Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant?

In a room where g = 9.81 m/s², a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally. The height of the platform above the ground is 2.00 m. What is the speed of the puck just before it hits the ground? The air resistance is negligibly small.

The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to

You are traveling at 55 mi/h along the +x-axis relative to a straight, level road and pass a car that is traveling at 45 mi/h. The relative velocity of your car to the other car is

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

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?

The magnitude of $\vec { A }$ is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 ° with the +y-axis. The components of $\vec { A }$ are closest to:

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 boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the horizontal distance to the point where the football hits the ground if we neglect air resistance?

The figure shows four vectors, $\vec { A }$ , $\overrightarrow { \mathbf { B } }$ , $\overrightarrow { \mathrm { C } }$ , and $\vec { D }$ . Vectors $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ each have a magnitude of 7.0 cm, and vectors $\overrightarrow { \mathrm { C } }$ and $\vec { D }$ each have a magnitude of 4.0 cm. Find the x and y components of the sum of these four vectors.

Two perpendicular vectors, $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ , are added together giving vector $\overrightarrow { \mathrm { C } }$ . If the magnitudes of both vectors $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ are doubled without changing their directions, the magnitude of vector $\overrightarrow { \mathrm { C } }$ will

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

Enzo throws a rock horizontally with a speed of 12 m/s from a bridge. It falls for 2.28 s before reaching the water below with no appreciable air resistance. Just as the rock reaches the water, find (a) the horizontal component of its velocity. (b) the speed with which it is moving.

Vector $\vec { A }$ has a magnitude of 4.0 m and points 30° south of east. Vector $\overrightarrow { \mathbf { B } }$ has a magnitude of 2.0 m and points 30° north of west. The resultant vector $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ is given by

Shown below are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to its right?

As shown in the figure, a projectile is fired at time t = 0.00 s, from point 0 at the upper edge of a cliff, with initial velocity components of $v 0 x = 30 \mathrm {~m} / \mathrm { s }$ and $v 0 y = 300 \mathrm {~m} / \mathrm { s }$ The projectile rises and then falls into the sea at point P. The time of flight of the projectile is $75.0 \mathrm {~s} ,$ and air resistance is negligible. At this location, g = 9.80 m/s². What is the horizontal distance D?

A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal. Neglecting air resistance, what is horizontal component of the projectile's acceleration?