1
VECTORS
~ has a magnitude of 8units and make an angles of 45◦ with the positive x-axis.
1- Vector A
~ also has the same magnitude of 8units and directed along the negative x-axis. find
Vector B
~+B
(a) The magnitude of A ~
~−B
(b) The magnitude of A ~
~ has a magnitude of 35.0 units and points in the direction 325 counterclockwise from
2-Vector A
the positive x axis. Calculate the x and y components of this vector.
3-A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north,
and then 6.00 blocks east.
(a) What is her resultant displacement?
(b) What is the total distance she travels?
~ and B
4- Use the component method to add the vectors A ~ shown in Figure 1.1. Both vectors
~ makes an angle of 30.0 with the x axis. Express the
have magnitudes of 3.00m and vector A
~+B
resultant A ~ in unit-vector notation.
Fig. 1.1:
5-The helicopter view in Figure 1.2 shows two people pulling on a stubborn mule. The person
on the right pulls with a force F~1 of magnitude 120N and direction of θ1 = 60.0. The person on
the left pulls with a force F~2 of magnitude 80.0N and direction of θ2 = 75.0. Find
VECTORS
(a) the single force that is equivalent to the two forces shown and
(b) the force that a third person would have to exert on the mule to make the resultant force
equal to zero. The forces are measured in units of newtons (symbolized N).
Fig. 1.2:
~ = (3î − 3ĵ)m, B
6- Consider the three displacement vectors A ~ = (î − 4ĵ)mandC
~ = (−2î + 5ĵ)m.
Use the component method to determine
~ =A
(a) the magnitude and direction of D ~+B
~ +C
~
~ = −A
(b) the magnitude and direction of E ~−B
~ +C
~
~ and B
7-Two vectors A ~ have the same magnitude of 5 units and they start from the origin: B
~
~ points to the South West exactly opposite to vector B.
points to the North East and A ~ What
would be the magnitude of the resultant vector? Why?
8- If two vectors have equal magnitude, what are the maximum and minimum magnitudes of
their sum?
9-Is it possible to add a vector quantity to a scalar quantity? Explain.
10-Can the magnitude of a vector have a negative value? Explain.
11-. A book is moved once around the perimeter of a table top with the dimensions 1.0 m by
2.0 m. The book ends up at its initial position.
(a) What is its displacement?
(b) What is the distance traveled?
~ has x and y components of 28.70cm and 15.0cm, respectively; vector B
12-Vector A ~ has x and y
~ −B
components of 13.2cm and 26.60cm, respectively. If A ~ + 3C
~ = 0, what are the components
~ ?
of C
~ = 20units
13- Three displacement vectors of a croquet ball are shown in Figure 1.3, where |A|
~ = 40units, and |C|
, |B| ~ = 30units. Find
2
VECTORS
(a) the resultant in unit vector notation and
(b) the magnitude and direction of the resultant displacement.
Fig. 1.3:
14-A man pushing a mop across a floor causes it to undergo two displacements. The first has
a magnitude of 150cm and makes an angle of 120◦ with the positive x axis. The resultant
displacement has a magnitude of 140cm and is directed at an angle of 35◦ to the positive x axis.
Find the magnitude and direction of the second displacement.
15-A person going for a walk follows the path shown in Figure 1.4. The total trip consists of
four straight line paths. At the end of the walk, what is the persons resultant displacement
measured from the starting point?
Fig. 1.4:
~ = 6î + 2ĵ − k̂ and N
16- Given M ~ = 2î − ĵ − 3k̂ calculate the M
~ .N
~, M
~ ∗N
~ and the angle between
~ andN
M ~
17-If the cross product of two vectors is equal to zero, what can you say about their directions?
~ with A
18-What is the dot product of vector A ~ ∗ B?
~
3
2
Kinematics
1-One drop of oil falls straight down onto the road from the engine of a moving car every 5s.
Figure OQ2.1 shows the pattern of the drops left behind on the pavement. What is the average
speed of the car over this section of its motion?
Fig. 2.1:
2- A cannon shell is fired straight up from the ground at an initial speed of 225m/s. After how
much time is the shell at a height of 6.20 ∗ 102 m above the ground and moving downward?
3- An arrow is shot straight up in the air at an initial speed of 15.0m/s. After how much time
is the arrow moving downward at a speed of 8.00m/s?
4- A rock is thrown downward from the top of a 40.0 − m-tall tower with an initial speed of
12m/s. Assuming negligible air resistance, what is the speed of the rock just before hitting the
ground?
5- On another planet, a marble is released from rest at the top of a high cliff. It falls 4.00m in
the first 1s of its motion. Through what additional distance does it fall in the next 1s?
6-If the average velocity of an object is zero in some time interval, what can you say about the
Kinematics
displacement of the object for that interval?
7-If a car is traveling eastward, can its acceleration be westward? Explain.
8- If the velocity of a particle is zero, can the particles acceleration be zero? Explain. 9-The
position versus time for a certain particle moving along the x axis is shown in Figure 1.6. Find
the average velocity in the time intervals 10- A particle moves according to the equation x = 10t2 ,
Fig. 2.2:
where x is in meters and t is in seconds.
(a) Find the average velocity for the time interval from 2.00 s to 3.00 s.
(b) Find the average velocity for the time interval from 2.00 to 2.10 s.
