### 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

**Very short answer questions**

- Define a) Unit vector b) Null vector c) Co-planar vector
- 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.
- A projectile is fired at an angle of 45
^{o}and reaches the highest point in its path in 2√2 If air resistance is neglected, find the maximum height reached by it. - A boy can throw a ball 40 m vertically upward. find the greatest horizontal distance he can throw by the boy.
- 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.
- 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.
- 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.
- 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.
- Derive the relation between linear velocity and angular velocity.
- 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.
- A body starts rotating from rest and completes 20 revolutions in 4 sec. Find its angular acceleration.

**Short answer questions**

- Define dot product and give its properties.
- Derive an expression for a) Maximum height b) Horizontal range for a projectile.
- Discuss about cross product and mention its properties.
- Can we add a vector quantity to a scalar quantity?
- What is the relation between horizontal range and time of flight?
- 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 45
^{o}with the horizontal, then find the initial velocity of the stone. - 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.
- 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.
- 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.
- 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**

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

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