### Motion in a plane class 11 important questions

MOTION IN A PLANE

Topics to be focused in this lesson

• Scalar product
• Resultant of vectors
• Projectile motion
• Uniform circular motion
1. Define a) Unit vector  b) Null vector    c) Co-planar vector
2.  The vector A has a magnitude of 5 unit, B has a magnitude of 6 unit and the cross product A and B has the magnitude of 15 unit. Find the angle between A and B.
3. A projectile is fired at an angle of 45o and reaches the highest point in its path in 2√2 If air resistance is neglected, find the maximum height reached by it.
4. A boy can throw a ball 40 m vertically upward. find the greatest horizontal distance he can throw by the boy.
5. The speed of a projectile at its maximum height is 6 m/s. If it stays in the air for a total time of 8 seconds, find its horizontal range.
6. A projectile is thrown to have maximum horizontal range on the ground. Find the ratio of the horizontal and vertical components of its initial velocity.
7. Two stones are thrown each with a velocity of g from the same point in opposite directions on the ground. If each has the greatest horizontal range, their separation on reaching the ground.
8.  A boat takes 4 hr upstream and 2 hr downstream for covering the same distance. Find the ratio of velocity of boat to the water in river.
9. Derive the relation between linear velocity and angular velocity.
10. In 20 seconds, the speed of a motor changes from 1200 rpm to 1800 rpm. In this period of time, find the number of revolutions completed by motor.
11. A body starts rotating from rest and completes 20 revolutions in 4 sec. Find its angular acceleration.
1. Define dot product and give its properties.
2. Derive an expression for a) Maximum height b) Horizontal range for a projectile.
3. Discuss about cross product and mention its properties.
4. Can we add a vector quantity to a scalar quantity?
5. What is the relation between horizontal range and time of flight?
6. From the top of a building 20 m high, a ball is projected horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of 45o with the horizontal, then find the initial velocity of the stone.
7. Two paper screens A and B are separated by a distance of 100 m. A bullet pierces screen A and then screen B. The hole in B is 10 cm below in A. If the bullet is travelling horizontally at A, then find its velocity at A.
8.  The angular velocity of a wheel increases from 120 rpm to 480 rpm in 10 sec. Calculate the number of revolutions made during this time.
9. The width of a river is 2√3 km. A boat is rowed in direction perpendicular to the banks of river. If the drift of the boat due to flow is 2 km, find the displacement of the boat.
10. The vehicle of a wheel rotating with certain angular velocity is stopped in 7 seconds and before it stops, it makes 35 revolutions. Then what is the initially frequency with which the wheel was rotating?

Essay questions
1. Prove that the path of the projectile is a parabola.
2. State parallelogram law of vectors. Derive an expression for the magnitude of the resultant vector.
3. Derive expressions for the maximum height and horizontal range and obtain the relation between them.