- Vectors in Physics
- |
- Two Dimensional Motion
- |
- Motion in a plane with constant acceleration
- |
- Relative Velocity in two dimension
- |
- Projectile Motion
- |
- Uniform circular motion
- |
- Motion in three dimensions
- |
- Sample Problems with Solutions

The radius vector of point x relative to origin varies with time as

$\mathbf{r}=a cos(kt)\mathbf{i}+b sin(kt)\mathbf{j}$

Where a and b are constants and i and j are vectors along x and y axis. Which one of the following is the mean velocity vector?

a. $ \frac {a cos(kt)\mathbf{i}- b sin(kt)\mathbf{j}}{t}$

b. $a cos(kt)\mathbf{i}+ b sin(kt)\mathbf{j}$

c. $a cos(kt)\mathbf{i}- b sin(kt)\mathbf{j}$

d. $ \frac {a cos(kt)\mathbf{i}+ b sin(kt)\mathbf{j}}{t}$

Solution

A wind is blowing in the North direction at the speed of 5 km/hr. An airplane moves to a point in the East which is 2000 km away in 40 hr. Find the velocity of the airplane with respect to the wind.

Solution

Two cars A and B run at constant speed $u_1$ and $u_2$ along the highways intersecting at an angle $\theta$. They start at t=0 at the intersection point. Find the time required to have distance s between the two cars

Solution

A bar XY of length l which always remains in the same vertical plane has its ends X and Y constrained to remain in contact with the horizontal floor and in vertical wall as shown below in the figure.

The bar starts from a vertical position and end X is moved along the floor with a constant velocity v

(a) Ellipse

(b) Circle

(c) Parabola

(d) Straight line

Solution

Three particles of mass m

Solution

Two particles X and Y travel along the x and y axis with respective velocities

$\mathbf{v_1} = 2\mathbf{i}$ m/sec

$\mathbf{v_2} = 3\mathbf{j}$ m/sec

At t=0 they are at

$x_1 = -3m$ and $y_1=0$

$x_2= 0$ and $y_2=-3 m$

Find the vector which represents the position of Y relative to X as a function of t

i and j are respective unit vectors along x and y direction

a. $(3t -3) \mathbf{j} + (3-2t) \mathbf{i}$

b. $(3t +3) \mathbf{j} + (3+2t) \mathbf{i}$

c. $(3t -2) \mathbf{j} + (2-2t) \mathbf{i}$

d. None of the above

Solution

The system is shown below in Figure

The ring X moves with constant velocity v downwards. The angle AXY is θ. Find the velocity of the ring Y

Solution

Find the velocity of ring Y with respect to ring X

Solution

If he wishes to land on the other bank at a point directly across the river from his starting point

Velocity of man with respect to the person standing on the bank

a. 5 m/s

b. 10 m/s

c. 6 m/s

d. $5 \sqrt {3}$ m/s

Solution

Find the angle made by the man from the current

a. 120°

b. 60°

c. 30°

d. 90°

Solution

Find the time taken by the man to cross the river

Solution

what direction it should swim

a. 90° to current

b. 30° to current

c. 60 ° to current

d. none of these

Solution

How much time

a. 5

b. 10

c. 6

d. 4

Solution

How much distance it will land from his starting point

a. 30

b. 20

c. 25

d. none of these

Solution

Find the rectangular components of the average velocity in the time interval between $t$ and $t + \Delta t$

Solution

Which of the following statements are true about the motion

a. The particle is experiencing uniform acceleration motion

b. The particle starts at y axis and touched x axis in 1sec

c. The initial velocity is towards negative Y axis

d. The velocity at t=1 is towards positive x axis

Solution

$y=x^2$

So that at any time $v_x=3 m/s$

Find the magnitude and direction of velocity at x=1/3 m

Solution

Find the acceleration at x=1/3 (both magnitude and direction)

a. 18 m/sec

b. 14 m/sec

c. 18 m/sec

d. 14 m/sec

Solution

Class 11 Maths Class 11 Physics Class 11 Chemistry

Thanks for visiting our website.

**DISCLOSURE:** THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU DECIDE TO MAKE A PURCHASE THROUGH MY LINKS, AT NO COST TO YOU. PLEASE READ MY **DISCLOSURE** FOR MORE INFO.