Exam 3: Vectors and Motion in Two Dimensions

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

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.

On a calm day with no wind, you can run a 1500-m race at a velocity of 4.0 m/s. If you run the same race on a day when you have a constant headwind that slows your speed by 2.0 m/s, how much time would it take you to finish the race?

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 stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff if air resistance is negligibly small?

You walk $33 \mathrm {~m}$ to the north, then turn 60° to your right and walk another $45 \mathrm {~m} .$ How far are you from where you originally started?

A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s². The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before the projectile hits the level ground?

The x component of vector $\overrightarrow { \mathrm { A } }$ is 5.3 units, and its y component is -2.3 units. The angle that vector $\overrightarrow { \mathrm { A } }$ makes with the +x-axis is closest to

Your motorboat can move at 30 km/h in still water. What is the minimum time it will take you to move 12 km downstream in a river flowing at 6.0 km/h?

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 $\overrightarrow { \mathrm { A } }$ - $\overrightarrow { \mathrm { B } }$ - $\overrightarrow { \mathrm { C } }$ .

A vector in the xy-plane has an x component of -7.50 units. What must be the y component of this vector so that its magnitude is 10.0 units. (Note: There are two possible answers.)

Enzo throws a rock horizontally with a speed of 12 m/s from a bridge. It falls for 2.28 s before reaching the water below with no appreciable air resistance. Just as the rock reaches the water, find (a)the horizontal component of its velocity. (b)the speed with which it is moving.

If vector $\overrightarrow { \mathrm { A } }$ has components A_x = -3.0 lb and A_y = -4.0 lb, and vector $\overrightarrow { \mathrm { B } }$ has components B_x = 3.0 lb and B_y = -8.0 lb, what is the magnitude of vector $\overrightarrow { \mathrm { C } }$ = $\overrightarrow { \mathrm { A } }$ - $\overrightarrow { \mathrm { B } }$ ?

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

A runner runs on a circular path of radius 10 m. What is the magnitude of the displacement of the jogger if he runs (a)half-way around the track? (b)all the way around the track?

A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s². The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what angle was the projectile fired above the horizontal?

A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m, as shown in the figure. The width of the pylon is very narrow, and the length of each propeller blade is 12 m. A tip of the propeller breaks off just when the propeller is vertical. The fragment flies off horizontally, falls, and strikes the ground at point P with negligible air resistance. Just before the fragment broke off, the propeller was turning uniformly, taking 1.2 s for each rotation. How far is point P from the base of the pylon?

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?

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