Exam 3: Vectors and Motion in Two Dimensions

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.

Alicia intends to swim to a point straight across a 100 m wide river with a current that flows at 1.2 m/s. She can swim 2.5 m/s in still water. At what angle, measured from the upstream direction, must she swim upstream to achieve her goal?

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?

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

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?

A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

A projectile leaves the ground at 150 m/s and reaches a maximum height of 0.57 km. If there was no air resistance, at what angle above the horizontal did it leave the ground?

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s².

A ball rolls over the edge of a platform with a horizontal velocity of magnitude v. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the magnitude of v if air resistance is negligibly small?

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?

The magnitude of $\overrightarrow { \mathrm { A } }$ 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 $\overrightarrow { \mathrm { A } }$ are closest to:

Vector $\overrightarrow { \mathrm { A } }$ has a magnitude of 8.0 m and points east, vector $\overrightarrow { \mathrm { B } }$ 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 $\overrightarrow { \mathrm { A } }$ + $\overrightarrow { \mathrm { B } }$ + $\overrightarrow { \mathrm { C } }$ is given by

An object moves in a circular path at a constant speed. Compare the direction of the object's velocity and acceleration vectors.

The figure shows three vectors, $\overrightarrow { \mathrm { A } }$ , $\overrightarrow { \mathrm { B } }$ , and $\overrightarrow { \mathrm { C } }$ , along with their magnitudes. Determine the magnitude and direction of the vector given by $\overrightarrow { \mathrm { A } }$ + $\overrightarrow { \mathrm { B } }$ - $\overrightarrow { \mathrm { C } }$ .

The figure shows four vectors, $\overrightarrow { \mathrm { A } }$ , $\overrightarrow { \mathrm { B } }$ , $\overrightarrow { \mathrm { C } }$ , and $\overrightarrow { \mathrm { D } }$ , having magnitudes 10.0 m, 8.00 m, 6.00 m, and 2.00 m, respectively. Find the magnitude of the sum of these four vectors.

Find the magnitude and direction of the resultant of the three force vectors, $\overrightarrow { \mathrm { A } }$ , $\overrightarrow { \mathrm { B } }$ , and $\overrightarrow { \mathrm { C } }$ , shown in the figure. These vectors have the following magnitudes: A = 5.0 lb, B = 7.9 lb, and C = 8.0 lb. Express the direction of the resultant by specifying the angle it makes with the +x-axis, with counterclockwise angles taken to be positive.

A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally. The height of the platform above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect air resistance.

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

Which of the following statements are true about an object in two-dimensional projectile motion with no air resistance? (There could be more than one correct choice.)

The figure shows three vectors, $\overrightarrow { \mathrm { A } }$ , $\overrightarrow { \mathrm { B } }$ , and $\overrightarrow { \mathrm { C } }$ , having magnitudes 7.0 cm, 6.0 cm, and 4.0 cm, respectively. Find the x and y components of the resultant of these three vectors.