Exam 3: Vectors and Motion in Two Dimensions

In an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble is dropped from the same height. Compare the times of fall of the two pebbles.

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, $\vec { A }$ , $\overrightarrow { \mathbf { B } }$ , and $\overrightarrow { \mathrm { C } }$ , along with their magnitudes. Determine the magnitude and direction of the vector given by $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ - $\overrightarrow { \mathrm { C } }$ .

A cat leaps to try to catch a bird. If the cat's jump was at 60° off the ground and its initial velocity was $2.74 \mathrm {~m} / \mathrm { s }$ what is the highest point of its trajectory, neglecting air resistance?

A fisherman casts his bait toward the river at an angle of 25° above the horizontal. As the line unravels, he notices that the bait and hook reach a maximum height of $2.9 \mathrm {~m}$ What was the initial velocity he launched the bait with? Assume that the line exerts no appreciable drag force on the bait and hook and that air resistance is negligible.

The magnitude of a vector can never be less than the magnitude of any of its components.

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?

Find the magnitude and direction of the resultant of the three force vectors, $\vec { A }$ , $\overrightarrow { \mathbf { B } }$ , 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.

Vector $\vec { A }$ has a magnitude of 8.0 m and points 30° north of east; vector $\overrightarrow { \mathbf { B } }$ has a magnitude of 6.0 m and points 30° west of north; and vector $\overrightarrow { \mathrm { C } }$ has a magnitude of 5.0 m and points 30° west of south. The resultant vector $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ + $\overrightarrow { \mathrm { C } }$ is given by

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?

James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. If there is no air resistance, when they reach the lake below

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?

The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is

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?

The components of vectors $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ are given as follows: A_x = 7.6 B_x = -5.1 A_y = -9.2 B_y = -6.8 What is the magnitude of the vector difference $\overrightarrow { \mathbf { B } }$ - $\vec { A }$ ?

A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal. What is the vertical component of its velocity after 4.0 s if air resistance is neglected?

When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was 1.8 m/s. What was the angle of the mountain surface above the horizontal?

Three forces, $\overrightarrow { \mathbf { F } }$ ₁, $\overrightarrow { \mathbf { F } }$ ₂, and $\overrightarrow { \mathbf { F } }$ ₃, each of magnitude 70 N, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is

Displacement vector $\vec { A }$ is 75 cm long and points at 30° above the +x-axis. Displacement vector $\overrightarrow { \mathbf { B } }$ 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 $\vec { A }$ . (b) Determine the x and y components of vector $\overrightarrow { \mathbf { B } }$ . (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 football kicker is attempting a field goal from $44 \mathrm {~m}$ out. The ball is kicked and just clears the lower bar with a time of flight of $2.9 \mathrm {~s}$ If the angle of the kick was 45°, what was the initial speed of the ball, assuming no air resistance?