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Motion in a plane

A hiker stands on the edge
of a cliff 490 m above the ground and
throws a stone horizontally with an initial
speed of 15 m s-1. Neglecting air resistance,
find the time taken by the stone to reach
the ground, and the speed with which it
hits the ground. (Take g = 9.8 m s-2 ).

Motion in a plane

Galileo, in his book Two new
sciences, stated that “for elevations which
exceed or fall short of 45° by equal amounts,
the ranges are equal”. Prove this statement.

Motion in a plane

A particle starts from origin
at t = 0 with a velocity 5.0 î m/s and moves
in x-y plane under action of a force which
produces a constant acceleration of
(3.0i
ɵ+2.0j
ɵ
) m/s 2
. (a) What is the
y-coordinate of the particle at the instant
its x-coordinate is 84 m ? (b) What is the
speed of the particle at this time ?

Motion in a plane

The position of a particle is
given by

r i j k = + + 3.0t
ˆ .
ˆ . 2 0 5 0 ˆ
2
t
where t is in seconds and the
coefficients have the proper units for r to
be in metres. (a) Find v(t) and a(t) of the
particle. (b) Find the magnitude and
direction of v(t) at t = 1.0 s.

Motion in a plane

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.

Motion in a plane

Find the magnitude and
direction of the resultant of two vectors A
and B in terms of their magnitudes and
angle θ between them.

Motion in a plane

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 ?

Mechanics

Define Newton’s first law of motion. Provide an example.

Motion in a plane

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 ?

Motion in a plane

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.