A motorboat is racing
towards north at 25 km/h and the water
current in that region is 10 km/h in the
direction of 60° east of south. Find the
resultant velocity of the boat.
Find the magnitude and
direction of the resultant of two vectors A
and B in terms of their magnitudes and
angle θ between them.
Rain is falling vertically with
a speed of 35 m s–1. Winds starts blowing
after sometime with a speed of 12 m s–1 in
east to west direction. In which direction
should a boy waiting at a bus stop hold
his umbrella ?
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at
a ground observation point by the aircraft positions 10.0 s a part is 30°, wat is the
speed of the aircraft ?
Read each statement below carefully and state, with reasons and examples, if it is
true or false :
A scalar quantity is one that
(a) is conserved in a process
(b) can never take negative values
(c) must be dimensionless
(d) does not vary from one point to another in space
(e) has the same value for observers with different orientations of axes.
For any arbitrary motion in space, which of the following relations are true :
(a) vaverage
= (1/2) (v (t
1
) + v (t
2
))
(b) v
average
= [r(t
2
) – r(t
1
) ] /(t
2
– t
1
)
(c) v (t) = v (0) + a t
(d) r (t) = r (0) + v (0) t + (1/2) a t
2
(e) a average
=[ v (t
2
) – v (t
1
)] /( t
2
– t
1
)
(The ‘average’ stands for average of the quantity over the time interval t
1
to t
2
)
ɵ
i
and ɵ
j are unit vectors along x- and y- axis respectively. What is the magnitude
and direction of the vectors ɵ ɵ
i j + , and ɵ ɵ
i j − ? What are the components of a vector
A= 2 ɵ ɵ
i j + 3 along the directions of ɵ ɵ
i j + and ɵ ɵ
i j − ? [You may use graphical method]
A particle starts from the origin at t = 0 s with a velocity of 10.0 jɵ m/s and moves in
the x-y plane with a constant acceleration of (8.0 2.0 )
ɵ ɵ
i j + m s-2. (a) At what time is
the x- coordinate of the particle 16 m? What is the y-coordinate of the particle at
that time? (b) What is the speed of the particle at the time ?
The position of a particle is given by
ˆ ˆ ˆ 2 r i j k = − + 3.0 2.0 4.0 m t t
where t is in seconds and the coefficients have the proper units for r to be in metres.
(a) Find the v and a of the particle? (b) What is the magnitude and direction of
velocity of the particle at t = 2.0 s ?
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