Exam 3: Vectors and Motion in Two Dimensions

The Moon is 3.84 × 10⁸ m from Earth and takes 27.3 days to complete each orbit. What are the magnitude and direction of the acceleration of the Moon, assuming a circular orbit?

The figure shows four vectors, $\overrightarrow { \mathrm { A } }$ , $\overrightarrow { \mathrm { B } }$ , $\overrightarrow { \mathrm { C } }$ , and $\overrightarrow { \mathrm { D } }$ . Vectors $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ both have a magnitude of 7.0 cm, and vectors $\overrightarrow { \mathrm { C } }$ and $\overrightarrow { \mathrm { D } }$ both have a magnitude of 4.0 cm. Find the magnitude and direction of the sum of these four vectors.

A player hits a tennis ball into the air with an initial velocity of 32 m/s at 35° from the vertical. How fast is the ball moving at the highest point in its trajectory if air resistance is negligible?

For general projectile motion with no air resistance, the horizontal component of a projectile's acceleration

Consider two vectors $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ shown in the figure. The difference $\overrightarrow { \mathrm { A } }$ - $\overrightarrow { \mathrm { B } }$ is best illustrated by A. B. C. D.

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

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?

A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is

You need to design a wheel for testing purposes such that its rim will have an acceleration of 1.5 g when the rim is moving at 37 m/s while spinning. What should be the diameter of this wheel?

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 boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the shore)in order to travel directly across the stream. (a)What is the speed of the current? (b)What is the resultant speed of the boat with respect to the shore?

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?

Displacement vector $\overrightarrow { \mathrm { A } }$ is 75 cm long and points at 30° above the +x-axis. Displacement vector $\overrightarrow { \mathrm { B } }$ is 25 cm long and points along the -x-axis. Displacement vector $\overrightarrow { \mathrm { C } }$ is 40 cm long and points at 45° below the -x-axis. (a)Determine the x and y components of vector $\overrightarrow { \mathrm { A } }$ . (b)Determine the x and y components of vector $\overrightarrow { \mathrm { B } }$ . (c)Determine the x and y components of vector $\overrightarrow { \mathrm { C } }$ . (d)Determine the x and y components of the resultant of these three vectors. (e)Determine the magnitude and direction of the resultant of these three vectors.

A plane has an airspeed of 142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity?

At target practice, a rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below if air resistance is negligible?

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

An object moves with a constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object?

If a satellite moves with constant speed in a perfectly circular orbit around the earth, what is the direction of the acceleration of the satellite?

A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground and experiences no appreciable air resistance as it moves. (a)How far from where the child is standing does the ball hit the ground? (b)How long is the ball in flight before it hits the ground? (c)What is the magnitude of the ball's velocity just before it hits the ground?

A plane moving 200 m/s horizontally fires a projectile with speed 50 m/s in a forward direction 30.0° below the horizontal. At that instant, what is the speed of the projectile with respect to a stationary observer on the ground?