# Motion in a plane Solved examples

## Numerical Questions

Question 1
A stone is thrown from ground level over horizontal ground. It just clears three walls, the successive distances between them being r and 2r. The inner wall is 15/7 times as high as the outer walls which are equal in height. The total horizontal range is nr, where n is an integer. Find n.

Question 2
A particle moves such that
x = (18.0)t
and y = 4t - 4.90t2
(a) Write a vector expression for the particle position as a function of time, using the unit vectorsi and j
(b) Obtain the expression for the velocity vector as a function of time
(c) Obtain the expression for the acceleration vector a as a function of time.
(d) Find the the position, the velocity, and the acceleration of the particle at t = 1.00 s.

## Multiple Choice Questions

Question 3
Which two quantities are constant throughout projectile motion when air resistance is negligible?
(a) The speed and acceleration.
(b) The vertical component of velocity and acceleration.
(c) The magnitude of the acceleration and the speed.
(d) The horizontal component of velocity and acceleration.
(e) The direction of the velocity and acceleration.

Question 4
A truck goes around a circular track of radius R at speed v so that it makes one circuit every T seconds As it does so it experiences a centripetal acceleration of magnitude p.If the truck now goes around a different circular track of radius 4R so that it now takes a time ½T to go around once, what is the magnitude of its centripetal acceleration?
(a) ½ p
(b) 16p.
(c) 4p.
(d) 8p.

Question 5
Which one of the following statements is true?
(a) A scalar quantity is the one that is conserved in a process.
(b) A scalar quantity is the one that can never take negative values.
(c) A scalar quantity is the one that does not vary from one point to another in space.
(d) A scalar quantity has the same value for observers with different orientations of the axes

Question 6
The component of a vector r along X-axis will have maximum value if
(a) r is along positive Y-axis
(b) r is along positive X-axis
(c) r makes an angle of 45° with the X-axis
(d) r is along negative Y-axis

Question 7
Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are
(a) Impulse, pressure and area
(b) Impulse and area
(c) Area and gravitational potential
(d) Impulse and pressure

Question 8
It is found that |A+B|=|A|.This necessarily implies,
(a) B = 0
(b) A,B are anti-parallel
(c) A,B are perpendicular
(d) $\mathbf{A}.\mathbf{B} \leq 0$

Question 9
if A= 3i + 4j and B= 7i + 24j. Which is of the below vector having the same magnitude as B and parallel to A
(a) 15i + 20j
(b) 15i - 20j
(c) 24i - 7j
(d) 7i - 24j

Question 10
For a particle performing uniform circular motion, choose the correct statement(s) from the following:
(a) Magnitude of particle velocity (speed) remains constant.
(b) Particle velocity remains directed perpendicular to radius vector.
(c) Direction of acceleration keeps changing as particle moves.
(d) Angular momentum is constant in magnitude but direction keeps changing

## Conceptual Questions

Question 11
A ball is thrown from a roof top at an angle of 30° above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have
(a) greatest speed.
(b) smallest speed.
(c) greatest acceleration?
Explain

Question 12
A football is kicked into the air vertically upwards. What is its
(a) acceleration at the highest point
(b) velocity at the highest point?

Question 13
What will the effect on horizontal range of a projectile when its initial velocity is doubled keeping the angle of projection same?

Question 14
Two spheres of 1 kg and 10 kg are dropped simultaneously from the same height . which sphere will reach the ground first?

Question 15
What is the angle between the direction of velocity and acceleration at the highest point of a projectile?

Question 16
a. Can a scalar quantity be added to vector quantity
b. Can the product of scalar quantity and vector quantity possible
c. Is the magnitude and direction same for A + B and B + A
d. Is the magnitude and direction same for A - B and B - A

## Numerical Questions

Question 17
A bomb is fired from a cannon with a velocity of 1000 m/s making an angle 30° with the horizontal
a. What is the time taken for the bomb to reach highest point
b. What is the time of flight
c. What is the maximum height reached
d. what is the range
Take g=9.8 m/s2

Question 18
The sum and difference of the two vectors are equal in magnitude
|A + B| = |A - B|
Prove that the vectors A and B are mutually perpendicular

Question 19
A bullet is fired from a gun at a speed of 5000 m/s. At what height should the gun be aimed above a goal if it has to strike the goal at a distance of 500 m? Take g=10m/s2

Question 20
A person sees a bird on a tree 39.6 m high and at a distance of 59.2 m. With what velocity the person should throw an arrow at an angle of 45° so that it may hit the bird?

## Text based Questions

Question 21
Define Centripetal acceleration and Derive an expression for centripetal acceleration for an body moving with uniform speed v along a circular path of radius r
Question 22
What is projectile motion. Derive the expression for Time of flight, Maximum height and Horizontal range
Question 23
Establish the relationship between linear velocity and angular velocity in a uniform circular motion
Question 24
Suppose you have two force F and F. How would you combine them in order to have a resultant force of magnitude
a. zero
b. 2 |F|
c. |F|

Question 25
Match the column