Exam 3: Vectors and Motion in Two Dimensions

A submarine must travel how fast (with respect to the water) and be pointed in what direction such that it moves 10 m/s directly northward (relative to the earth) if the water moves westward at 5.0 m/s?

An airplane is pointed at 45° north of east and is moving at 71 m/s with respect to the air. The jet stream (moving air) carries the plane at 30 m/s toward the east. What are the magnitude and direction of the velocity of the plane relative to the ground?

At a location where g = 9.80 m/s², a projectile returns to its original height after 4.08 seconds, during which time it travels 76.2 meters horizontally. If air resistance can be neglected, what was the projectile's initial speed?

Four vectors, $\vec { A }$ , $\overrightarrow { \mathbf { B } }$ , $\overrightarrow { \mathrm { C } }$ , and $\vec { D }$ , are shown in the figure. The sum of these four vectors is a vector having magnitude and direction

Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of diameter 60 m. What are the magnitude and direction of her acceleration?

A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter. What is the magnitude of the acceleration of the car?

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally and experiences no significant air resistance. The height of the platform above the ground is 2.0 m. What is the magnitude of the vertical component of the velocity of the puck just before it hits the ground?

The acceleration due to gravity on the Moon is only one-sixth of that on Earth, and the Moon has no atmosphere. If you hit a baseball on the Moon with the same effort (and therefore at the speed and angle) as on Earth, how far would the ball would travel on the Moon compared to on Earth? Neglect air resistance on Earth.

A player kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory

The figure shows four vectors, $\vec { A }$ , $\overrightarrow { \mathbf { B } }$ , $\overrightarrow { \mathrm { C } }$ , and $\vec { D }$ , having magnitudes 12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is

A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the heading of the plane in order to move directly eastward relative to the ground?

The figure shows two vectors $\overrightarrow { \mathbf { B } }$ and $\overrightarrow { \mathrm { C } }$ , along with their magnitudes and directions. The vector $\vec { D }$ is given by $\vec { D }$ = $\overrightarrow { \mathbf { B } }$ - $\overrightarrow { \mathrm { C } }$ . (a) What is the magnitude of vector $\vec { D }$ ? (b) What angle does vector $\vec { D }$ make with the +x-axis?

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

Vector $\vec { A }$ has a magnitude of 6.0 m and points 30° north of east. 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

A plane has an airspeed of 200 m/s northward, and is in a wind of 50.0 m/s to the west. The plane's speed relative to the ground is

Two forces are acting on an object as shown in the figure. Assume that all the quantities shown are accurate to three significant figures. (a) What is the magnitude of the resultant force on the object? (b) What is the direction of the resultant force?

Vectors $\overrightarrow { \mathbf { M } }$ and $\vec { N }$ obey the equation $\overrightarrow { \mathbf { M } }$ + $\vec { N }$ = 0. These vectors satisfy which one of the following statements?

If a vector $\vec { A }$ has components A_x > 0, and A_y < 0, then the angle that this vector makes with the positive x-axis must be in the range

Vector $\vec { A }$ has a magnitude of 8.0 m and points east, vector $\overrightarrow { \mathbf { B } }$ has a magnitude of 6.0 m and points north, and vector $\overrightarrow { \mathrm { C } }$ has a magnitude of 5.0 m and points west. The resultant vector $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ + $\overrightarrow { \mathrm { C } }$ is given by

Displacement vector $\vec { A }$ is 5.5 cm long and points along the +x-axis. Displacement vector $\overrightarrow { \mathbf { B } }$ is 7.5 cm long and points at +30° to the -x-axis. (a) Determine the x and y components of vector $\vec { A }$ . (b) Determine the x and y components of vector $\overrightarrow { \mathbf { B } }$ . (c) Determine the x and y components of the resultant of these two vectors. (d) Determine the magnitude and direction of the resultant of these two vectors.