Deck 3: Motion in a Plane

Question 1

A projectile is launched from the edge of a cliff with a velocity of $10.0 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees above the horizontal. What is the velocity of the projectile 2.00 seconds later (ignoring air resistance, and assuming it hasn't reached the ground yet)?

A) $V_{\mathrm{x}}=5.6 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-14.6 \mathrm{~m} / \mathrm{s}$
B) $\mathrm{V}_{\mathrm{x}}=14.6 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-5.6 \mathrm{~m} / \mathrm{s}$
C) $\mathrm{V}_{\mathrm{x}}=8.7 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-14.6 \mathrm{~m} / \mathrm{s}$
D) $\mathrm{V}_{\mathrm{x}}=-14.6 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=8.7 \mathrm{~m} / \mathrm{s}$
E) $\mathrm{V}_{\mathrm{x}}=-8.7 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-14.6 \mathrm{~m} / \mathrm{s}$

Answer 1

$\mathrm{V}_{\mathrm{x}}=8.7 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-14.6 \mathrm{~m} / \mathrm{s}$

Question 2

A projectile is launched from the edge of a cliff with a velocity of $15.0 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees above the horizontal. Ignoring air resistance, what is the velocity of the projectile 2.00 seconds later?

A) $11.4 \mathrm{~m} / \mathrm{s}$ at an angle of 43 degrees below the horizontal
B) $17.8 \mathrm{~m} / \mathrm{s}$ at an angle of 43 degrees below the horizontal
C) $17.8 \mathrm{~m} / \mathrm{s}$ at an angle of 38 degrees above the horizontal
D) $11.4 \mathrm{~m} / \mathrm{s}$ at an angle of 38 degrees below the horizontal
E) $17.8 \mathrm{~m} / \mathrm{s}$ at an angle of 43 degrees above the horizontal

Answer 2

$17.8 \mathrm{~m} / \mathrm{s}$ at an angle of 43 degrees below the horizontal

Question 3

A projectile is projected from the origin with a velocity of $30.0 \mathrm{~m} / \mathrm{s}$ at an angle of 45.0 degrees above the horizontal. What is the velocity and time when the projectile hits the ground?

A) $V_{\mathrm{x}}=16.7 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-16.7 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=3.33 \mathrm{~s}$
B) $V_{\mathrm{x}}=21.2 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-15.0 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=3.33 \mathrm{~s}$
C) $\mathrm{V}_{\mathrm{x}}=21.2 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-21.2 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=4.33 \mathrm{~s}$
D) $\mathrm{V}_{\mathrm{x}}=16.7 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-21.2 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=4.33 \mathrm{~s}$
E) $V_{x}=21.1 \mathrm{~m} / \mathrm{s}, V_{y}=-16.7 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=2.83 \mathrm{~s}$

Answer 3

$\mathrm{V}_{\mathrm{x}}=21.2 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-21.2 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=4.33 \mathrm{~s}$

Question 4

A projectile is projected from the origin with a velocity of $45.0 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees above the horizontal. What is the velocity when the projectile hits the ground?

A) $\mathrm{V}_{\mathrm{x}}=22.5 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-22.5 \mathrm{~m} / \mathrm{s}$
B) $\mathrm{V}_{\mathrm{x}}=35.7 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-22.5 \mathrm{~m} / \mathrm{s}$
C) $\mathrm{V}_{\mathrm{x}}=39.0 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-35.7 \mathrm{~m} / \mathrm{s}$
D) $V_{\mathrm{x}}=35.7 \mathrm{~m} / \mathrm{s}, \mathrm{V}_{\mathrm{y}}=-39.0 \mathrm{~m} / \mathrm{s}$
E) $V_{x}=39.0 \mathrm{~m} / \mathrm{s}, V_{y}=-22.5 \mathrm{~m} / \mathrm{s}$

Question 5

A projectile is projected from the origin with a velocity of $25.0 \mathrm{~m} / \mathrm{s}$ at an angle of 50.0 degrees above the horizontal. What is the time of maximum height of the projectile?

A) $3.01 \mathrm{~s}$
B) $2.67 \mathrm{~s}$
C) $1.95 \mathrm{~s}$
D) $2.03 \mathrm{~s}$
E) $3.45 \mathrm{~s}$

Question 6

A projectile is projected from the origin with a velocity of $20.0 \mathrm{~m} / \mathrm{s}$ at an angle of 60.0 degrees above the horizontal. What is the maximum height of the projectile?

A) $20.2 \mathrm{~m}$
B) $8.40 \mathrm{~m}$
C) $9.50 \mathrm{~m}$
D) $10.9 \mathrm{~m}$
E) $15.3 \mathrm{~m}$

Question 7

A projectile is projected from the origin with a velocity of $45.0 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees above the horizontal. What is the time it takes for the projectile to hit the ground?

A) $3.02 \mathrm{~s}$
B) $6.04 \mathrm{~s}$
C) $4.59 \mathrm{~s}$
D) $2.54 \mathrm{~s}$
E) $5.31 \mathrm{~s}$

Question 8

A projectile is projected from the origin with a velocity of $25.0 \mathrm{~m} / \mathrm{s}$ at an angle of 45.0 degrees above the horizontal. What is the time it takes for the projectile to hit the ground?

A) $2.22 \mathrm{~s}$
B) $1.95 \mathrm{~s}$
C) $3.04 \mathrm{~s}$
D) $3.61 \mathrm{~s}$
E) $2.75 \mathrm{~s}$

Question 9

A projectile is projected from the origin with a velocity of $30.0 \mathrm{~m} / \mathrm{s}$ at an angle of 40.0 degrees above the horizontal. What is the time it takes the projectile to reach maximum height?

A) $1.02 \mathrm{~s}$
B) $1.97 \mathrm{~s}$
C) $1.54 \mathrm{~s}$
D) $2.23 \mathrm{~s}$
E) $2.66 \mathrm{~s}$

Question 10

The velocity of a boat with respect to the water is $4.0 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees NORTH of WEST. The velocity of the water with respect to the ground is $8.0 \mathrm{~m} / \mathrm{s}$ at an angle of 45 degrees SOUTH of EAST. What is the velocity of the boat with respect to the ground?

A) $4.7 \mathrm{~m} / \mathrm{s}$ at 32 degrees SOUTH of WEST
B) $9.8 \mathrm{~m} / \mathrm{s}$ at 330 degrees SOUTH of EAST
C) $4.3 \mathrm{~m} / \mathrm{s}$ at 59 degrees SOUTH of EAST
D) $8.3 \mathrm{~m} / \mathrm{s}$ at 25 degrees SOUTH of WEST
E) $8.3 \mathrm{~m} / \mathrm{s}$ at 22 degrees SOUTH of WEST

Question 11

The velocity of a boat with respect to the water is $4.0 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees NORTH of EAST. The velocity of the water with respect to the ground is $3.0 \mathrm{~m} / \mathrm{s}$ at an angle of 90.0 degrees NORTH of EAST. What is the velocity of the boat with respect to the ground?

A) $5.8 \mathrm{~m} / \mathrm{s}$ at 36 degrees NORTH of EAST
B) $5.8 \mathrm{~m} / \mathrm{s}$ at 55 degrees NORTH of EAST
C) $6.1 \mathrm{~m} / \mathrm{s}$ at 61 degrees NORTH of EAST
D) $6.1 \mathrm{~m} / \mathrm{s}$ at 36 degrees NORTH of EAST
E) $6.1 \mathrm{~m} / \mathrm{s}$ at 55 degrees NORTH of EAST

Question 12

The velocity of an airplane with respect to the ground is $2.00 \times 102 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees NORTH of EAST. The velocity of the airplane with respect to the air is $1.50 \times 10^{2} \mathrm{~m} / \mathrm{s}$ at an angle of 60.0 degrees NORTH of EAST. What is the velocity of the air with respect to the ground?

A) $134 \mathrm{~m} / \mathrm{s}$ at 49 degrees SOUTH of EAST
B) $103 \mathrm{~m} / \mathrm{s}$ at 65 degrees NORTH of EAST
C) $103 \mathrm{~m} / \mathrm{s}$ at 17 degrees SOUTH of EAST
D) $134 \mathrm{~m} / \mathrm{s}$ at 17 degrees NORTH of EAST
E) $112 \mathrm{~m} / \mathrm{s}$ at 50 degrees NORTH of EAST

Question 13

The velocity of the air with respect to the ground is $50.0 \mathrm{~m} / \mathrm{s}$ at an angle of 30.0 degrees NORTH of EAST. The velocity of the airplane with respect to the air is $150 \mathrm{~m} / \mathrm{s}$ at an angle of 60.0 degrees NORTH of EAST. What is the velocity of the airplane with respect to the ground?

A) $195 \mathrm{~m} / \mathrm{s}$ at 53 degrees SOUTH of EAST
B) $195 \mathrm{~m} / \mathrm{s}$ at 53 degrees NORTH of EAST
C) $103 \mathrm{~m} / \mathrm{s}$ at 29 degrees SOUTH of EAST
D) $135 \mathrm{~m} / \mathrm{s}$ at 29 degrees SOUTH of EAST
E) $158 \mathrm{~m} / \mathrm{s}$ at 16 degrees NORTH of EAST

Question 14

Given that a vector extends from the origin to $(-5.0 \mathrm{~cm}, 8.0 \mathrm{~cm})$ , find the magnitude of the vector.

A) $-5.6 \mathrm{~cm}$
B) $9.4 \mathrm{~cm}$
C) $9.8 \mathrm{~cm}$
D) $3.4 \mathrm{~cm}$

Question 15

Given that a vector has components (120 m, $-60.0 \mathrm{~m})$ , find the direction of the vector relative to the positive $\mathrm{x}$ -axis.

A) $122^{\circ}$
B) $26.6^{\circ}$
C) $-26.6^{\circ}$
D) $116^{\circ}$

Question 16

A vector of magnitude 15.2 directed along the positive $x$ -axis combines with a second vector of magnitude 14.8 and unspecified direction. What is the minimum possible magnitude of the resultant total vector?

A) 14.8
B) 3.5
C) Not enough information is given.
D) 21.2
E) 15.0
F) 0.4

Question 17

What is the $x$ -component of a vector of magnitude 27.0 directed at $73^{\circ}$ counterclockwise from the negative $y$ -axis?

A) +7.9
B) +25.8
C) -8.3
D) -7.9
E) -25.8
F) +8.3

Question 18

The $y$ -component of a vector is -15.0 , while its magnitude is 27.2 . Which could be the vector's direction?

A) $33.5^{\circ}$ below the $-x$ -axis
B) $61.1^{\circ}$ below the $+x$ -axis
C) $28.9^{\circ}$ below the $+x$ -axis
D) $56.5^{\circ}$ below the $-x$ -axis
E) None of the choices are correct.

Question 19

A displacement vector $D$ is given as $40.0 \mathrm{~m}$ at an angle of 60.0 degrees NORTH of EAST. The $D_{x}$ component and the $\mathrm{D}_{\mathrm{y}}$ component of the vector are

A) $\mathrm{D}_{\mathrm{x}}=+20.0 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=+34.6 \mathrm{~m}$ .
B) $\mathrm{D}_{\mathrm{x}}=+34.6 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=-20.0 \mathrm{~m}$ .
C) $\mathrm{D}_{\mathrm{x}}=+34.6 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=+20.0 \mathrm{~m}$ .
D) $\mathrm{D}_{\mathrm{x}}=-34.6 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=+20.0 \mathrm{~m}$ .
E) $D_{\mathrm{x}}=+20.0 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=-34.6 \mathrm{~m}$ .

Question 20

A displacement vector $D$ is given as $40.0 \mathrm{~m}$ at an angle of 60.0 degrees EAST of NORTH. The $D_{x}$ component and the $\mathrm{D}_{\mathrm{y}}$ component of the vector are

A) $D_{\mathrm{x}}=+34.6 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=+20.0 \mathrm{~m}$ .
B) $\mathrm{D}_{\mathrm{x}}=+34.6 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=-20.0 \mathrm{~m}$ .
C) $\mathrm{D}_{\mathrm{x}}=-34.6 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=+20.0 \mathrm{~m}$ .
D) $\mathrm{D}_{\mathrm{x}}=+20.0 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=-34.6 \mathrm{~m}$ .
E) $\mathrm{D}_{\mathrm{x}}=+20.0 \mathrm{~m}, \mathrm{D}_{\mathrm{y}}=+34.6 \mathrm{~m}$ .

Question 21

An ant crawls in a straight line at a constant speed of $0.24 \mathrm{~m} / \mathrm{s}$ for a distance of $3.0 \mathrm{~m}$ , beginning in the corner of a square classroom. It then turns exactly 90 degrees to the right and proceeds an additional $4.0 \mathrm{~m}$ with a constant speed of $0.44 \mathrm{~m} / \mathrm{s}$ , reaching the other corner of the same wall from which it began. What was the ant's average speed for the full trip from corner to corner?

A) $0.21 \mathrm{~m} / \mathrm{s}$
B) $0.32 \mathrm{~m} / \mathrm{s}$
C) $0.23 \mathrm{~m} / \mathrm{s}$
D) $0.30 \mathrm{~m} / \mathrm{s}$
E) $0.34 \mathrm{~m} / \mathrm{s}$

Question 22

An ant crawls in a straight line at a constant speed of $0.24 \mathrm{~m} / \mathrm{s}$ for a distance of $3.0 \mathrm{~m}$ , beginning in the corner of a square classroom. It then turns exactly 90 degrees to the right, and proceeds an additional $4.0 \mathrm{~m}$ , reaching the far corner of the same wall from which it began. If the second leg of the journey was crawled in half the amount of time as the first, what was the ant's average speed for the whole trip?

A) $0.37 \mathrm{~m} / \mathrm{s}$
B) $0.44 \mathrm{~m} / \mathrm{s}$
C) $0.80 \mathrm{~m} / \mathrm{s}$
D) $0.27 \mathrm{~m} / \mathrm{s}$

Question 23

The interstate on-ramp is $1.5 \mathrm{~km}$ west of your home, and on leaving for grandmother's house you are only able to accomplish an average velocity of $12 \mathrm{~km} / \mathrm{hr}$ between your home and the on-ramp. At the on-ramp, you wait for traffic for $2.0 \mathrm{~min}$ before proceeding toward grandmother's house. If you wish to arrive there, which is $15 \mathrm{~km}$ south of the on-ramp, over a river and through some woods, in a total elapsed time of 25.0 minutes, what average speed must you maintain on the interstate highway?

A) $58 \mathrm{~km} / \mathrm{hr}$
B) $51 \mathrm{~km} / \mathrm{hr}$
C) $67 \mathrm{~km} / \mathrm{hr}$
D) none of these

Question 24

The interstate on-ramp is $5.5 \mathrm{~km}$ west of your home, and on leaving for grandmother's house you are only able to accomplish an average velocity of $38 \mathrm{~km} / \mathrm{hr}$ between your home and the on-ramp. At the on-ramp, you wait for traffic for $2.0 \mathrm{~min}$ before proceeding toward grandmother's house. If you wish to arrive there, which is $15 \mathrm{~km}$ south of the on-ramp, over a river and through some woods, having achieved an average velocity of $42 \mathrm{~km} / \mathrm{hr}$ for the whole trip, how fast do you need to drive south on the interstate highway?

A) $48 \mathrm{~km} / \mathrm{hr}$
B) $58 \mathrm{~km} / \mathrm{hr}$
C) $74 \mathrm{~km} / \mathrm{hr}$
D) $39 \mathrm{~km} / \mathrm{hr}$