Motion in a plane Position and Displacement Vectors

Motion in a plane

Position and Displacement Vectors

Free and localized vectors

Equality of vectors

Unit Vectors

Addition and subtraction of vectors

Vector Parallelogram Method

Analytical solution of vector addition

Special cases of addition of two vectors

Resolution of Vectors

Addition and subtraction of vectors considering unit vectors

Law of Cosines and sines of vectors

Multiplications of vectors

Scalar product

Properties of scalar product

Vector Product

Vector Product in terms of rectangular unit vectors

Some properties of unit vectors

Quantities related to motion of an object in a plane

Motion in a plane with constant acceleration

Relative motion in two dimensions

Projectile motion

Projectile motion

Equation of trajectory of inclined projectile

Time of flight, Horizontal Range and Maximum height of an inclined projectile

Horizontal Projectile

Trajectory of projectile

Trajectory of projectile

Velocity of projectile

Time of flight of horizontal projectile

Horizontal Range

Uniform Circular Motion

Uniform Circular Motion

A stone is thrown from ground level over horizontal ground. It just clears three walls, the successive distances between them being r and 2 r. 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.

A particle moves such that x = (18. 0)t and y = 4 t - 4. 90 t 2 (a) Write a vector expression for the particle position as a function of time, using the unit vectors i 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 position, the velocity, and the acceleration of the particle at t = 1. 00 s.

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?

A football is kicked into the air vertically upwards. What is its (a) acceleration at the highest point (b) velocity at the highest point? • Solution: At highest point, velocity becomes zero and acceleration remains same as acceleration due to gravity

What will the effect on horizontal range of a projectile when its initial velocity is doubled keeping the angle of projection same? • See the mathematical equation

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

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 • a. No b. Yes c. Yes d. False. Magnitude is same but direction is opposite

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=10 m/s 2

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| • a. Anti-parallel b. Parallel c. both at an angle of 120°

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? • Solve it?

Assignments

Assignments