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Exam 3: Vectors and Motion in Two Dimensions

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Question 91

Multiple Choice

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A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level?

A) 4.0 m/s
B) 8.0 m/s
C) 16 m/s
D) 9.8 m/s

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Question 92

Multiple Choice

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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) 202 m/s
B) 9.80 m/s
C) 19.6 m/s
D) 45.2 m/s
E) 94.4°

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Question 93

Short Answer

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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?

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?

You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

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 boy throws a rock with an initial velocity of $3.13 \mathrm {~m} / \mathrm { s }$ at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s²?

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?

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

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? $\begin{array}{llcc}& \text { Northward } & \text { } &\\ \underline{\text { choice}} & \underline{\text { component}}&\underline{\text { component}} \\ \text { 1 } &29.4m& 17.0m \\ \text {2 } &18.2m&28.1m\\ \text { 3} &22.4m&11.5m\\ \text {4 } &17.0m&27.4m\\ \text { 5 } &25.2m&18.2m\\\end{array}$

A batter hits a home run in which the ball travels 110 m horizontally with no appreciable air resistance. If the ball left the bat at 50° above the horizontal just above ground level, how fast was it hit?

Consider two vectors $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ shown in the figure. The difference $\vec { A }$ - $\overrightarrow { \mathbf { B } }$ is best illustrated by (a) (b) (c) (d)

A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance?

If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude.

The components of vectors $\overrightarrow { \mathbf { B } }$ and $\overrightarrow { \mathrm { C } }$ are given as follows: $B _ { x }$ = -9.2 $C _ { x }$ = -4.5 $B _ { y }$ = -6.1 $C _ { y }$ = 4.3 The angle (less than 180°) between vectors $\overrightarrow { \mathbf { B } }$ and $\overrightarrow { \mathrm { C } }$ is closest to

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

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 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?

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?

A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?