Exam 3: Vectors and Motion in Two Dimensions

Four vectors, $\overrightarrow { \mathrm { A } }$ , $\overrightarrow { \mathrm { B } }$ , $\overrightarrow { \mathrm { C } }$ , and $\overrightarrow { \mathrm { D } }$ , are shown in the figure. The sum of these four vectors is a vector having magnitude and direction

A celebrating student throws a water balloon horizontally from a dormitory window that is 50 m above the ground. It hits the ground at a point 60 m from the building without appreciable air resistance. (a)What will be the horizontal component of the velocity of the balloon just before it hits the ground? (b)What will be the magnitude of the vertical velocity of the balloon just before it hits the ground?

Two forces are acting on an object as shown in the figure. Assume that all the quantities shown are accurate to three significant figures. (a)What is the magnitude of the resultant force on the object? (b)What is the direction of the resultant force?

A boulder rolls off of a very high cliff and experiences no significant air resistance. While it is falling, its trajectory is never truly vertical.

A projectile is shot horizontally at 23.4 m/s from the roof of a building 55 m tall and experiences negligible air resistance. (a)Determine the time necessary for the projectile to reach the ground below. (b)Determine the distance from the base of the building that the projectile lands. (c)Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground.

A marble moving 1.48 m/s rolls off the top edge of a 125-cm high table in a room where there is no appreciable air resistance and the acceleration due to gravity is 9.80 m/s². (a)How far from the base of the table will it strike the floor? (b)How long will it be in the air?

Vector $\overrightarrow { \mathbf { M } }$ = 4.00 m points eastward and vector $\overrightarrow { \mathrm { N } }$ = 3.00 m points southward. The resultant vector $\overrightarrow { \mathbf { M } }$ + $\overrightarrow { \mathrm { N } }$ is given by

A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

A 5.0-kg stone is thrown upward at 7.5 m/s at an angle of 51° above the horizontal from the upper edge of a cliff, and it hits the ground 1.5 s later with no air resistance. Find the magnitude of its velocity vector just as it reaches the ground.

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?

You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance. After 2.0 s, the magnitude of the velocity of the rock is closest to

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

A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football?

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later with no air drag. (a)How fast was it thrown? (b)How far from its original position did it land? (c)How high above its original position did it go?

Three forces, $\overrightarrow { \mathbf { F } }$ ₁, $\overrightarrow { \mathbf { F } }$ ₂, and $\overrightarrow { \mathbf { F } }$ ₃, all act on an object, as shown in the figure. The magnitudes of the forces are: F₁ = 80.0 N, F₂ = 60.0 N, and F₃ = 40.0 N. The resultant force acting on the object is given by

You walk 53 m to the north, then you turn 60° to your right and walk another $45 \mathrm {~m} .$ Determine the direction of your displacement vector. Express your answer as an angle relative to east.

Vector $\overrightarrow { \mathrm { A } }$ has a magnitude of 6.0 m and points 30° south of east. Vector $\overrightarrow { \mathrm { B } }$ has a magnitude of 4.0 m and points 30° west of south. The resultant vector $\overrightarrow { \mathrm { A } }$ + $\overrightarrow { \mathrm { B } }$ is given by

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

The magnitude of a vector an only zero if all of its components are zero.

Vector $\overrightarrow { \mathrm { A } }$ has a magnitude of 6.0 m and points 30° north of east. Vector $\overrightarrow { \mathrm { B } }$ has a magnitude of 4.0 m and points 30° west of north. The resultant vector $\overrightarrow { \mathrm { A } }$ + $\overrightarrow { \mathrm { B } }$ is given by