Instructions: Answer all questions on the "Scantron" sheet. Fill in your name last name first. (Your Student Number is not required). Also fill in the pledge. Some problems call for number answers, and some for letter answers. Read the scantron sheet accordingly (no difference between capital and lower case letters).
Answers are in bold. Comments in red for the problems most frequently missed
A = (A cosq)i + (A sinq) jA ·B = AB cosq = AxBx + AyByA2 = A ·A = Ax2 + Ay2 = A2
g = 9.8 m/s2 ar = v2/r T = 2pr/v
h =
vi2 sin2qi
2g
=
vyi2
2g
R =
vi2 sin(2qi)
g
=
2vxi vyi
g
Geometry:
A juggler throws two balls to the same height so that one is at the halfway point going up when the other is at the halfway point coming down. At that point:
Their velocities and accelerations are equal.
Their velocities are equal but their accelerations are equal and opposite.
Their accelerations are equal but their velocities are equal and opposite.
Their velocities and accelerations are both equal and opposite.
Their velocities are equal to their accelerations.
Is it possible for the velocity and the acceleration of an object to have opposite signs?
yes
no
Vx is the velocity of a particle moving along the x axis as shown on the right. If x = 5.0 m at t = 1.0 s, what is the position of the particle at t = 6.0 s? (mark the one digit of answer)
x = 5 - 3 = 2 m
A particle moving along the x axis has a position given by
x = (½bt2 - ct4) m,
where b and c are constants and t is measured in s. Consequently the time t at which its velocity is zero is given by
tn = b/4c. What is n? (Mark one digit answer)
n = 2
Therefore the acceleration a of the particle at the instant when its velocity is zero is given by a formula of the type
a = - (numerical factor)×(letter). Mark the numerical factor.
By differentiating the blue equation twice we get a = b - 12ct² at any time t. At the time of question 4, t² = b/4c, so a = b - 12c(b/4c) = - 2 b
Mark the letter in the formula of question 5. The letter is b
A skier leaves a ski jump with a horizontal velocity of 30 m/s. The instant before she lands 3.1 seconds later,
what is the magnitude of the horizontal component of her velocity? (Mark only first digit of answer)
vx = 30 m/s
What is the magnitude of the vertical component of her velocity at that instant? (Mark only first digit of answer)
vy = gt = 30.4 m/s
How far from the jumping-off point is she when she lands, measured along the slope? (Mark only first digit of answer)
v = (v_x t + ½gt²)½ = 140 m = 1.4×10² m
Mark exponent that goes with answer to question 9 The exponent is 2
If two collinear vectors A and B are added, the resultant has a magnitude equal to 4.0. If B is subtracted from A, the resultant has a magnitude equal to 8.0. What is the magnitude of B? (Mark one digit answer) -2
If the component of vector A along the vector B is zero, what can you conclude about these two vectors?
A
The vectors have equal magnitudes and are opposite in direction.
The vectors are perpendicular.
The vectors have the same direction.
The vectors have unequal magnitudes and are opposite in direction.
The angle between the vectors is 45°.
Is is possible to add a vector quantity to a scalar quantity?
yes
no
If vector C is added to vector D, the result is a third vector that is perpendicular to D and has a magnitude equal to 3D. What is the ratio of the magnitude of C to that of D?
1.3
1.6
1.8
2.2
3.2 The first "geometry" figure in the formula collection on the first page illustrates just this situation, so the answer is 10½.
Vectors A and B both have magnitude 2. The angle between them is 60°.
What is their scalar product A · B? (Mark one digit answer) A · B = 2×2×cos 60° = 2
A rock is thrown upward from the level ground in such a way that the maximum height of its flight
is equal to half its horizontal range. At what angle is the rock thrown? Specify this initial slope of the trajectory
by marking the ratio of velocity components, vy/vx (Mark one digit answer)
So h = ½R. From the formulas this says vyi2/2g = ½(2vxi vyi/g) and vyi/vxi = 2
A carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride?
5.7 m/s² downward
4.1 m/s² upward centripetal
14 m/s² downward
4.1 m/s² downward
19 m/s² downward
A basketball player who is 2.00 m tall shoots the ball at the basket, which is at a height of 3 m above the floor. The initial speed of the ball is 6.7 m/s. Neglect air resistance. What will be the speed of the ball when it reaches the basket? (Mark first digit of answer)
A car travels in a due northerly direction at a speed of 55 km/h. The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal. If the rain is falling vertically with respect to the earth, what is the speed of the rain with respect to the earth?
32 km/h
48 km/h
58 km/h
80 km/h
95 km/h Horizontal speed of rain (with respect to car) is 55 km/h. When vertical speed v is added, result must be at 60 degrees, so v/55 = Ö3 v = 95.3 km/h
A projectile starts at the coordinate origin, where the displacement vector also originates. The initial velocity makes an angle less than 90º with the horizontal. At the instant when the projectile is at the highest point of its trajectory, the displacement, velocity and acceleration vectors are r, v and a. Which statement is true?
