Exam 3: Vectors and Motion in Two Dimensions

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.

Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum

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

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 55° with the vertical. What is the length of the athlete's jump if air resistance is of no significance?

A child is trying to throw a ball over a fence. She gives the ball 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 the fence is 2.0 m high. The ball just clears the fence while still traveling upwards and experiences no significant air resistance. How far is the child from the fence?

A boat, whose speed in still water is 8.0 m/s, crosses a river with a current of 6.0 m/s. If the boat heads perpendicular to the current, what is the speed of the boat relative to an observer standing on the shore as it crosses the river?

The x component of vector $\overrightarrow { \mathrm { A } }$ is 8.7 units, and its y component is -6.5 units. The magnitude of $\overrightarrow { \mathrm { A } }$ is closest to

Three ropes are tied in a knot as shown in the figure. One student pulls on rope A with 1.0 pound of force, and another student pulls on rope B with 7.0 pounds of force. How hard and in what direction must you pull on rope C to balance the first two pulls? Give the direction by specifying the angle (clockwise or counterclockwise)of the pull with the direction of rope A.

A child sits on a merry-go-round, 1.5 meters from the center. The merry-go-round is turning at a constant rate, and the child is observed to have a radial acceleration of 2.3 m/s². How long does it take for the merry-go-round to make one revolution?

If a vector $\overrightarrow { \mathrm { A } }$ 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

Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the following statements are true about just before the snowballs reach the ground below? (There could be more than one correct choice.)

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

An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 35° above the horizontal. How long does the athlete stay in the air, assuming no significant air resistance?

A ball is thrown with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

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

A displacement vector is 34.0 m in length and is directed 60.0° east of north. Selecting from the choices in the table below, what are the components of this vector? Northward Eastward 1 29.4 17.0 2 18.2 28.1 3 22.4 11.5 4 17.0 29.4 5 25.2 18.2

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?

The maximum acceleration a pilot can stand without blacking out is about 7.0 g. In an endurance test for a jet plane's pilot, what is the maximum speed he can tolerate if he is spun in a horizontal circle of diameter 85 m?

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

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. Compare the time it takes each to reach the lake below if there is no air resistance.