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1. (15 points) You are given two vectors:

A

has length 10. and an angle of 60.o (with respect to the +x axis).

B

has length 10. and an angle of 200.o (with respect to the +x axis).

a) Calculate the components of both vectors, and write them in the blank lines below (4 pts).

A

= __________ i + __________ j B

= __________ i + __________ j

b) Construct and clearly present the resulting vector from the addition of A

plus B

(i.e.,

BAR

) on the coordinate system above and give the values of the components in terms of

unit vectors i and j in the blank lines below. (5 pts.)

R

= __________ i + __________ j

c) Find the scalar (dot) product BA

. (3 pts.)

d) Find the vector (cross) product BA

. (3 pts.)

x

10

10

10

10

y

15

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2. (18 points) A model rocket with a parachute recovery system is launched (from rest on the ground) straight up.

The rocket first accelerates at 4.00 m/s2 directly upwards for 3.00 s. Then the engine shuts off and the

rocket moves in “free fall” for 2.00 s. At this point a parachute comes out and the rocket quickly (you

may assume immediately) slows down to a terminal speed of 4.48 m/s.

a) How high above the ground (in meters) is the rocket when its engine shuts off? (3 pts.)

b) What is the maximum height above the ground reached by the rocket (in meters)? (4 pts.).

c) How high above the ground is the rocket when its parachute opens? (4 pts.)

d) How long does it take the rocket to float to the ground after its parachute opens? (4 pts.)

e) Sketch the velocity of the rocket for each of the three phases of flight below. (3 pts)

Accelerates

Upwards

Engine off Parachute out

t

v

18

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3. (14 points)

You want to throw a (puffy harmless) snowball at a

friend and hit her/him in the shoulder. Your friend is

standing 1.50 m below you a distance of 10.0 m

away, as marked with the X on the figure to the right.

You throw the snowball horizontally with an initial

velocity of vo. You can ignore air resistance.

a) Calculate the time the ball is in the air. (5 pts)

b) Calculate the needed initial velocity, vo, for the ball to exactly hit the person in the shoulder.

(5 pts.)

c) Using your chosen coordinate system (must clearly mark on figure above), sketch the x and y

position of the ball versus time during its motion in the air. (4 pts.)

x

t

y

t

vo

10 m

1.50 m

g

X

14

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4. (15 points)

You are a pilot who takes a small airplane out for a flight. Your airplane travels at 190 km/h in still air

and you decide to fly (in the air) in a direction exactly south-east (i.e., at an angle of 45o south of east).

The wind is blowing due north at 50 km/h.

a) Draw the complete velocity vector diagram (below) for this situation, including the velocity of

the airplane with respect to the ground. Clearly label and identify each velocity vector. (3 pts.)

b) What is your velocity vector with respect to the ground (in component form)? (6 pts.)

c) After one hour of flying, what distance and direction, did you travel with respect to the

ground? (6 pts.)

15

E (or +x) W

N (or +y)

S

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5. (22 points)

A block of mass m1, on an incline

with angle is attached to another

block of mass m2, on a flat surface,

with a massless rope that passes over

a frictionless ring. A large horizontal

force, F, pulls mass m2 to the right,

as shown in the figure. The

coefficient of kinetic friction, k,

between the blocks and surfaces is

the same everywhere.

a) Draw the free body diagrams (i.e. indicate all forces acting on each block) and write the

corresponding Newton’s Force equations-of-motion for that block. Clearly indicate your

choice of axes on the free body diagrams. (13 pts.)

Problem 5 continues on the next page.

m1 m2

m1 g

m2 F

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Problem 5 continued.

b) Solve for the acceleration of the system in terms of the horizontal force F, m1, m2, k, , and g.

(5 pts.)

c) Calculate the minimum horizontal force F needed to pull both blocks to the right at constant

speed given the following values: m1=10.0 kg, m2=20.0 kg, k=0.200, = 25o and g = 9.8

m/s2. (4 pts.)

22

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6. (16 points)

You attach a mass, m = 0.500 kg , to a L =1.0 m long rope and swing it around your head. The rope

(which you can assume is massless) makes an angle of with respect to the horizontal, as shown

in the figure.

a) In the “Side View” figure above, clearly show all the forces acting on the mass. Include the

acceleration vector in the figure. (3 pts.)

b) Calculate the speed of the mass (in m/s) for the given quantities. (6 pts.)

c) What is the period of this motion? (3 pts.)

d) What is the tension in the rope? (4 pts.)

16

v

Top View Side View

m m

L

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