Imagine yourself in a rain steadily falling vertically with a speed of 2ms-1. a) If you start moving with 1ms-1 due east, in which direction should you hold the umbrella to protect yourself from the rain? b) On a sunny day at 12 noon, you hold the umbrella vertically. If you run at certain speed, do you need to incline the umbrella? Justify your answer.
Motion along a plane is called two-dimensional motion. A body moving in two dimensions is found to have acceleration in one dimension. a) Identify the motion. b) A ball thrown by a player reaches another player reaches another player in 2s. What is the maximum height attained by the ball above the point of projection? (Take g = ms-2 ). c) In the figure, the point ‘P’ on a wheel of radius ‘R’ is in contact with the ground. What is the displacement of the point, when the wheel rolls a half revolution?
A parallelogram law helps to find the magnitude and direction of the resultant of two forces: a) State the law. b) If the magnitude of two vectors and their resultant are the same, what is the angle between the two vectors? c) Determine the value of (A - B) x ( A + B ). where A and B are vectors.
A boy throws a cricket ball with a velocity u at an angle θ with the horizontal. a) Name the path followed by the ball. b) At the highest point, what are the vertical and horizontal components of velocity? c)Derive an expression for the maximum height reached by the ball. (d) In the given figure, If θ1 = 300 , what is the value of θ2 ?
The outer side of a circular track of radius 200 m is raised to make an angle of 150 with the horizontal. a) Which force provides the necessary centripetal force for a car taking the circular track? b) Name the process by which the outer side of a curved track is raised a little above the inner side. c) Using the data provided in this case, determine the maximum permissible speed to avoid skidding (given µs = 0.25)
An athlete jumps at an angle of 300 with a maxim um speed of 9.4 m/s. a) What is the shape of the path followed by the athlete in the jump? b) Obtain an expression to calculate the horizontal range covered by the athlete. c) Find the range covered by him in the above jump. Suggest the angle by which the athlete
can attain the maximum range.
A stone is thrown with the help of a sling with initial velocity v0 at an angle θ from the horizontal. a) Working of sling is based on ........… law of vector addition. b) With the help of a vector diagram, state this law. c) Derive the expression for the maximum height reached by the stone.
When a body is projected into air with certain initial velocity making an angle with the horizontal, it will travel in a parabolic path. a) What are the vertical and horizontal components of velocity? b) With a diagram, derive an expression for : i. Maximum height ii. Time of flight. c) A ball is dropped through the window of a train travelling with high velocity, to a man standing near the track. The ball..........… i.Falls down vertically ii.Moves straight horizontally iii.Follows an elliptical path iv.Follows a parabolic path
a) Choose the correct statement / statements related to uniform circular motion. i) The acceleration in uniform circular motion is tangential to the circle. ii) The acceleration in uniform circular motion is directed radially inwards iii) The velocity in uniform circular motion has constant magnitude iv) The velocity in uniform circular motion is directed radially inwards b) A particle is projected up into air from a point with a speed of 20 m/s at an angle of projection 30o . What is the maximum height reached by it ?
(a) Figure shows the path of an object in Uniform Circular Motion. Redraw the figure and mark the directions of velocity and acceleration of the particle at P (b) An object moving uniformly in a circular path of radius 12 cm completes 7 revolutions in 100s. What is the angular speed, and the linear speed of the motion?
(a)
Draw / state velocity as tangent acceleration towards centre (b)
ω = 2 π f = 0.44 Rad / sec
v = rω = 0.053 m/s
The position vector r of a particle P located in an x-y plane is shown in figure. (a) Redraw the figure by showing the rectangular components . (b) Write the position vector in terms of rectangular components. (c) Write an equation to find the magnitude of the resultant of two vectors A and B.
The figure shows three paths for a football kicked from ground level with same velocity. Ignore the effects of air resistance. (a) Derive an equation for the maximum height of this football. (b) In which path the horizontal component of velocity is maximum ?
