Practice Quiz 2 - 2D Kinematics and Free Body Diagrams

(Chapter 3A) Two dimensional vector A has an x component of -10.65 and a y component of 6.15. What's the magnitude of vector A?

12.3

(Chapter 3A) A vector has a length of 4.0 units, is located in the second quadrant, and makes a 30 degree angle with respect to the y axis. What's the x and y component of the vector?

a) - 2.0, -3.5

b) -2.0, 3.5

c) -3.5, 2.0

d) 3.5, 2.0

b) -2.0, 3.5

(Chapter 3A) Vector A has an x component and a y component equal in magnitude. What's the angle that vector A makes with respect to the x axis in the same x-y coordinate system?

a) 90 degrees

b) 60 degrees

c) 45 degrees

d) 0 degrees

e) 120 degrees

c) 45 degrees

(Chapter 3A) Vectors A, B, and C have the given components:

Ax = 4.0, Ay = 8.0

Bx = 8.0, By = -7.0

Cx = 5.0, Cy = 6.0

Find the components of the combinations of these vectors:

(A + B)x =

(A + B)y =

(A -4C)x =

(A - 4C)y =

(A + B - C)x =

(A + B - C)y =

(A + B)x = 12

(A + B)y = 1.0

(A -4C)x = -16

(A - 4C)y = -16

(A + B - C)x = 7.0

(A + B - C)y = -5.0

(Chapter 3A) What are the magnitudes of the change in velocity and its angle theta if the initial velocity is 40.0 m/s south and the final velocity is 85.0 m/s west? Let angle theta be measured relative to the east direction (theta = 90 degrees means the change in velocity vector points north, theta = 180 degrees means the velocity vector points west, etc.).

Change in velocity = 93.9

Angle theta = 155 degrees

(Chapter 3A) A speedboat moves on a lake with initial velocity vector V(1,x) = 8.17 m/s and V(1,y) = -2.05 m/s, then accelerates for 6.99 s at an average acceleration of a a(av,x) = -0.105 m/s^2 and a(av,y) = 0.109 m/s^2.

a) What are the components of the speedboat's final velocity, V(2,x) and V(2,y)?

b) Find the speedboat's final speed.

a) V(2,x) = 7.44 m/s

V(2,y) = -1.29 m/s

b) V2 = 7.55 m/s

(Chapter 3A) Vector C has a magnitude of 23.4 m and points in the y direction. Vectors A and B both have positive y-components, and make angles of a = 44.9 degrees and b=29.2 degrees with the x axis, respectively. If the vector sum A+B+C = 0, what are the magnitudes of A and B?

A = 21.3 m

B = 17.2 m

(Chapter 3A) Vector A has a magnitude of 15.1 and its direction is 320 degrees counter-clockwise from the +x axis. What are the x and y components of the vector?

Ax = 11.6

Ay = -9.71

(Chapter 3A) A farmer builds three sections of a fence where L = 40.00m, and gets tired. Walking straight back to where he started, how far did he have to go?

d = 74.64

(Chapter 3A) The colored lines in the figure represent paths taken by different people walking around in a city. Assume that each city block is 110 m long.

a) What is the total distance traveled by the person walking along path A?

b) Calculate the magnitude and direction of the displacement vector of path A. (Direction should be counterclockwise up from due east)

a) 440 m

b) magnitude: 350 m

direction: 72 degrees

(Chapter 3B) A zookeeper is trying to shoot a monkey sitting at the top of a tree with a tranquilizer gun. If the monkey drops from the tree at the same instant that the zookeeper fires, where should the zookeeper hit the monkey? (Neglect any effects due to air resistance)

a) aim straight at the monkey

b) aim lower than the monkey

c) aim higher than the monkey

d) aim to the right of the monkey

a) aim right at the monkey

(Chapter 3B) In 1970 NBA championship, Jerry West made a 60ft shot from beyond half court to lead the LA Lakers to an improbable tie at the buzzer with the NY Knicks. Suppose West threw the ball at an angle of 50.0 degrees above the horizontal. The basket is 10 ft from the court floor. Neglecting air resistance, estimate the initial speed of the ball.

Initial speed = 13.5

(Chapter 3B) A tiger leaps horizontally out of a tree that is 3.80 m high. If he lands 5.10 m from the base of the tree, calculate his initial speed Vo. (Neglect air resistance)

Vo = 5.80 m/s

(Chapter 3B) A Chinook salmon can jump out of water with a speed of 6.50 m/s. How far horizontally d can this salmon travel through the air if it leaves the water with an initial angle of theta = 25 degrees with respect to the horizontal? (Let the horizontal direction the fish travels in be the +x direction, and let the upward vertical direction be the +y direction).

d = 3.30 m

(Chapter 3B) Two golf balls are hit from the same point on a flat field. Both are hit at an angle of 30 degrees above the horizontal. Ball 2 has twice the initial speed of ball 1. If ball 1 lands a distance d1 from the initial point, at what distance d2 does ball 2 land from the initial point?

a) d2 = 0.5d1

b) d2 = 2d1

c) d2 = 4d1

d) d2 = d1

e) d2 = 8d1

c) d2 = 4d1

(Chapter 3B) Robin would like to shoot an orange in a tree with his bow and arrow. The orange is hanging yf = 5.00 m above the ground. On his first try, Robin looses the arrow at Vo = 33.0 m/s at an angle of theta = 30.0 degrees above the horizontal. The arrow has an initial height of yo = 1.50 m, an its tip is x = 43.0 m away from the target orange.

a) Treating the arrow as a point projectile and neglecting air resistance, what's the height of the arrow once it has reached the horizontal position x of the orange?

b) How far from the orange should Robin stand in order to hit the orange? There may be more than one answer.

a) 48.3 m

b) 11.8 m

c) 84.3 m

d) 6.5 m

e) 89.6 m

a) height of arrow = 15.2 m

b) d) 6.5 m and e) 89.6m

(Chapter 3B) A projectile is fired at Vo = 420.0 m/s at an angle of theta = 71.0 degrees, with respect to the horizontal. Assume that air friction will shorten the range by 30.1%. How far will the projectile travel in the horizontal direction, R?

distance traveled: 7500 m

(Chapter 3B) a) The surface of the pool table is h = 0.730 m from the floor. The winner of the billiard competition wants to know if he has broken the world speed record for the break shot of 14.3 m/s. If the winner's ball landed a distance d = 3.95 m from the table's edge, calculate the speed of his break shot Vo. Assume friction is negligible.

b) At what speed v1 did his pool ball hit the ground?

a) Vo = 10.2 m/s

b) V1 = 10.9 m/s

(Chapter 3B) An airplane releases a ball as it flies parallel to the ground at a height of h = 215 m. If the ball lands on the ground a horizontal distance equal to the height h from the release point, calculate the speed v of the plane. Neglect any effects due to air resistance.

v = 32.5 m/s

(Chapter 3B) Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the beach below with a long measuring tape. Bob is a pitcher and he knows that the fastest he can throw the ball is about Vo = 35.3 m/s. Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial trajectory), and watches carefully. The ball rises and then falls, and after t1 = 0.710 s the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball landed x = 121 m from the base of the cliff. How high up is Bob, if the ball started exactly 2 m above the edge of the cliff?

Bob's position (height of cliff): 44 m

(Chapter 3B) Suppose a wheel with a tire on it is rotating at the constant rate of 2.39 times a second. A tack is stuck in the tire at a distance of 0.301 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack's tangential speed and centripetal acceleration.

Tangential speed: 4.52 m/s

centripetal acceleration: 67.9 m/s^2

(Chapter 3B) In a lab test of tolerance for high acceleration, a pilot is swung in a circle of 15.0 m in diameter. It's found that the pilot blacks out when he is spun at 30.6 rpm (rev/min).

a) At what acceleration does the pilot black out?

b) Express this acceleration in terms of a multiple of g.

c) If you want to decrease the acceleration by 18.0% without changing the diameter of the circle, by what percent must you change the time for the pilot to make one circle?

a) 77.0 m/s^2

b) 7.85 g

c) percent of time change: 9.5%

(Chapter 3B) Anne is working on a research project that involves the use of a centrifuge. Her samples must first experience an acceleration of 100g, but then, acceleration must increase by a factor of ten. By how much will the rotational speed have to increase? Express your answer as a fraction of the initial rotation rate.

rotational speed increase: 3.162

(Chapter 3B) In a vertical dive, a peregrine falcon can accelerate at 0.6 times the free fall acceleration g in reaching a speed of about 117 m/s. If a falcon pulls out of a dive into a circular arc at this speed and can sustain a radial acceleration of 0.6g, what's the radius R of the turn?

R = 2.33 km

(Chapter 3B) A device for acclimating military pilots to the high accelerations they must experience consists of a horizontal beam that rotates horizontally about one end while the pilot is seated at the other end. In order to achieve a radial acceleration of 25.9 m/s^ with a beam of length 5.73 m, what rotation frequency is required?

rotation frequency; 0.338 Hz (cycles per second)

During the sudden impact of a car accident, a person's neck can experience abnormal forces, resulting in an injury commonly known as whiplash. If the victim's head and neck move violently backwards, his car was hit from the

a) rear

b) front

c) left side

d) right side

a) rear

As a tractor pulls a plot across a field, it exerts a force on the plot in the forward direction. What's the "equal and opposite force" in this interaction, according to Newton's third law?

a) the force of the plow pushing forwards on the ground

b) the force of the ground pushing backwards on the plow

c) the force of the plow pulling backward on the tractor

d) the force of the tractor pushing backwards on the ground

c) the force of the plow pulling backward on the tractor

Case A in the figure is a block that is accelerated across a frictionless table by hanging a 10 N block (1.02 kg). In case B, the same block is accelerated by a steady 10 N tension in the string. Treat the masses of the strings as negligible. The block's acceleration in case B is...

a) twice its acceleration in case A

b) equal to its acceleration in case A

c) half its acceleration in case A

d) greater than its acceleration in case A

e) less than its acceleration in case A

d) greater than

How does the magnitude of the normal force exerted by the ramp in the figure compare to the weight of the static block?

The normal force is...

a) possible greater than or less than the weight of the block, depending on whether or not the ramp surface is smooth

b) equal to the weight of the block

c) possibly greater than or equal to the weight of the block, depending on whether or not the ramp surface is smooth

d) less than the weight of the block

e) greater than the weight of the block

c) less than the weight of the bkock

Consider four cases displaying the free-body diagram of a cyclist on a bike rolling down a hill (cyclist is not peddling) (look at screenshot). Treat the cyclist and bike as a single mass and consider air resistance. Select the free body diagram that correctly displays the external forces acting on the cyclist and the bike.

Case D