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# Worksheet on Motion In A Plane

Q1 For a given angle of projection if the initial velocity is doubled the range of the projectile becomes :-

a) half

b) one-fourth

c) two times

d) four times

Q2 A ball is projected to attain the maximum range. If the height attained is H, the range is:-

a) H

b) 2H

c) 4H

d) H/2

Q3 Two projectiles are fired from the same point with the same speeds at angles of projection 60 degree and 30 degree respectively. Which one of the following is true ?

a)Their horizontal ranges will be the same

b) Their maximum heights will be the same

c) Their landing velocities will be the same

d) Their times of flight will be the same

Q4 A ball is projected upwards from the top of a tower with a velocity of 50 m/s making an angle of 30 degree with the horizontal. The height of the tower is 70m. After how much time from the instant of throwing, will the ball reach the ground ?

a) 2 s

b) 5 s

c) 7 s

d) 9 s

Q5 An aeroplane moving horizontally with a speed of 180 km/h drops a food packet while flying at a height of 490 m. The horizontal range of the packet is :

a)180 m

b) 980 m

c) 500 m

d) 670 m

Q6 From the top of a tower 19.6 m high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of 45 degree with the horizontal, then the initial velocity of the ball is :

a) 9.8 m/s

b) 4.9 m/s

c) 14.7 m/s

d) 2.8 m/s

Q7 Assertion :- A body dropped from a given height and another body projected horizontally from the same height strike the ground simultaneously.

Reason :- Horizontal velocity has no effect in the vertical direction.

a) A

b) B

c) C

d) D

Q8 Assertion :- In a projectile motion, the acceleration is constant in both magnitude and direction but the velocity changes in both magnitude and direction.

Reason :- When a force or acceleration is acting in an oblique direction to the direction of velocity, then both magnitude and direction of the velocity may be changed.

a) A

b) B

c) C

d) D

Q9 Assertion :- In a projectile motion the projectile hits the ground with the same velocity with which it was thrown.

Reason :- In a projectile motion horizontal velocity remains same but vertical velocity continuously changes and particle strikes the ground with same vertical velocity with which the particle was thrown vertical direction

a) A

b) B

c) C

d) D

Q10 Assertion :- In a projectile motion, the vertical velocity of the particle is continuously decreased during its ascending motion.

Reason :- In projectile motion downward constant acceleration is present in vertical direction .

a) A

b) B

c) C

d) D

Q11 Assertion :- The trajectory of an object moving under constant acceleration due to gravity can be a straight line or parabola.

Reason :- Initial conditions affect the motion of the object.

a) A

b) B

c) C

d) D

Q12 The range of a projectile when fired at 75 degree to the horizontal is 0.5 km. What will be its range when fired at 45 degree with the same speed ?

a) 0.5 km

b) 1.0 km

c) 1.5 km

d) 2.0 km

Q13 If R is the maximum horizontal range of a particle, then the greatest height attained by it is :

a) R

b) 2R

c) R/2

d) R/4

Q14 A projectile is thrown from a point in a horizontal plane such that its horizontal and vertical velocity components are 9.8 m/s and 19.6 m/s respectively. Its horizontal range is :

a) 4.9 m

b) 9.8 m

c) 19.6 m

d) 39.2 m

Q15 A projectile is thrown into space so as to have the maximum possible horizontal range equal to 400m. Taking the point of projection as the origin, the coordinates of the point where the velocity of the projectile is minimum are :

a) (400, 100) m

b) (200, 100) m

c) (400, 200) m

d) (200, 200) m

Q16 A particle is projected at an angle of 45 degree , 8m away from the foot of a wall, just touches the top of the wall and falls on the ground on the opposite side at a distance 4m from it. The height of wall is :

a) 2/3 m

b) 4/3 m

c) 8/3 m

d) 3/4 m

Q17 Three particles A, B and C are projected from the same point with the same initial speeds making angles 30 degree , 45 degree and 60 degree respectively with the horizontal. Which of the following statements are correct ?

a) A, B and C have unequal ranges

b) Ranges of A and C are equal and less than that of B

c) Ranges of A and C are equal and greater than that of B

d) A, B and C have equal ranges

Q18 At the uppermost point of a projectile its velocity and acceleration are at an angle of :-

a) 80 degree

b) 90 degree

c) 60 degree

d) 45 degree

Q19) Define Tensor and give example?

Q20) Why current is a scalar even it possess direction?

Q21) Why pressure is a scalar even it possess direction?

Q22) Why the path of one projectile as seen from another projectile is a straight line?

1) d

2) c

3) a

4) c

5) c

6) a

7) a

8) a

9) d

10) a

11) a

12) b

13) d

14) d

15) b

16) c

17) b

18) b

19) Tensor : A quantity that has different values in different directions is called tensor.

Example : Moment of Inertia

​Note: A scalar is a zero rank tensor, and a vector is a first rank tensor.

20) Electric current is not a vector as it does not obey the law of vector addition.

21) Pressure possess multiple directions. For a quantity to be a vector, it should possess only one direction.

22) The path of one projectile as seen from another projectile is a straight line as relative acceleration of one projectile w.r.t. another projectile is zero.