Free Printable Vector Motion In Straight Line Projectile Motion

1.

A body moves over one fourth of a circular arc in a circle of radius r. The magnitude of distance travelled and displacement will be respectively:

a)

$\frac{\pi r}{2},r\sqrt[]{2}$

b)

$\frac{\pi r}{4},r$

c)

$\pi r,\frac{r}{\sqrt[]{2}}$

d)

$\pi r,r$

2.

An aeroplane flies 400 m north and 300 m south and then flies 1200 m upwards then net displacement is:

a)

1200 m

b)

1300 m

c)

1400 m

d)

1500 m

3.

If a car covers 2/5th of the total distance with v₁speed and 3/5th distance with v2 then average speed is:

a)

$\frac{1}{2}\sqrt[]{v_1}v_2$

b)

$\frac{v_1+v_2}{2}$

c)

$\frac{2v_1v_2}{v_1+v_2}$

d)

$\frac{5v_1v_2}{3v_1+2v_2}$

4.

The relation $3t=\sqrt[]{3x+6}$ describes the displacement of a particle in one direction where x is in metres and t in sec. The displacement, when velocity is zero, is:

a)

24 metres

b)

12 metres

c)

5 metres

d)

Zero

5.

The motion of a particle is described by the equation $x=a+bt^2$ where a =15cm and b = 3cm. Its instantaneous velocity at time 3 sec will be:

a)

36 cm/sec

b)

18 cm/sec

c)

16 cm/sec

d)

32 cm/sec

6.

A car moving on a straight road covers one third of the distance with 20 km/hr and the rest with 60 km/hr. The average speed is:

a)

40 km/hr

b)

80 km/hr

c)

$46\frac{2}{3}$ km/hr

d)

36 km/hr

7.

If displacement of a particle is directly proportional to the square of time. Then particle is moving with:

a)

Uniform acceleration

b)

Variable acceleration

c)

Uniform velocity

d)

Variable acceleration but uniform velocity

8.

A body starts from the origin and moves along the x-axis such that velocity at any instant is given by $\left(4t^3-2t\right)$ where t is in second and velocity is in m/s. What is the acceleration of the particle, when it is 2m from the origin?

a)

28 m/s²

b)

22 m/s²

c)

12 m/ s²

d)

10 m/s²

9.

he diagram shows the displacement-time graph for a particle moving in a straight line. The average velocity for the interval t = 0, t = 5 is:

a)

0

b)

6 ms^-1

c)

-2 ms^-1

d)

2 ms^-1

10.

Figure shows the displacement time graph of a body. What is the ratio of the speed in the first second and that in the next two seconds?

a)

1 : 2

b)

1 : 3

c)

3 : 1

d)

2 : 1

11.

A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity υ. The two bodies meet after a time t. The value of t is:

a)

$\frac{2v}{a}$

b)

$\frac{v}{a}$

c)

$\frac{v}{2a}$

d)

$\sqrt[]{\frac{v}{2a}}$

12.

A student is standing at a distance of 50metres from the bus. As soon as the bus starts its motion with an acceleration of 1 ms –2, the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the students is able to catch the bus is:

a)

5 ms^-1

b)

8 ms^-1

c)

10 ms^-1

d)

12 ms^-1

13.

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is:

a)

6m

b)

12m

c)

18m

d)

24m

14.

The average velocity of a body moving with uniform acceleration travelling a distance of 3.06 m is 0.34 ms ^–1. If the change in velocity of the body is 0.18ms^–1during this time, its uniform acceleration is:

a)

0.01 ms ^–2

b)

0.02 ms ^–2

c)

0.03 ms ^–2

d)

0.04 ms ^–2

15.

A particle travels 10m in first 5 sec and 10m in next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec:

a)

8.3 m

b)

9.3 m

c)

10.3 m

d)

None of above

16.

The trajectory of a projectile is represented by $y=\sqrt[]{3x}+gx^2$ /2 The angle of projection is:

a)

30º

b)

45º

c)

60º

d)

None of these

17.

The path followed by a body projected along the y-axis is given as by $y=\sqrt[]{3x}-\left(\frac{1}{2}\right)x^2$ , if g = 10 m/s, then the initial velocity of projectile will be – (x and y are in m)

a)

$3\sqrt[]{10\ }$ m/s

b)

$2\sqrt[]{10}$ m/s

c)

$10\sqrt[]{3}$ m/s

d)

$10\sqrt[]{2}$ m/s

18.

In a projectile motion, velocity at maximum height is:

a)

$\mu\ \frac{\cos\theta}{2}$

b)

$\mu\ \cos\ \theta$

c)

$\mu\ \frac{\sin\theta}{2}$

d)

None of these

19.

A body is thrown at angle 30º to the horizontal with the velocity of 30 m/s. After 1 sec, its velocity will be (in m/s) (g = 10 m/s ² )

a)

$10\sqrt[]{7}$

b)

$700\sqrt[]{10}$

c)

$100\sqrt[]{7}$

d)

$\sqrt[]{40}$

20.

Two seconds after projection a projectile is travelling in a direction inclined at 30º to the horizontal after one more sec, it is travelling horizontally, the magnitude and direction of its velocity are:

a)

$2\sqrt[]{20}$ m/sec,60º

b)

$20\sqrt[]{3}$ m /sec, 60º

c)

$6\sqrt[]{40}$ m/sec, 30º

d)

$40\sqrt[]{6}$ m /sec, 30º

21.

a)

40ms ^-`1

b)

$40\sqrt[]{2}$ ms^-1

c)

20ms^-1

d)

$20\sqrt[]{2}$ ms^-1

22.

A projectile is thrown with an initial velocity of $v=aiˆ+bjˆ$ , if the range of a projectile is double the maximum height reached by it then:

a)

a = 2b

b)

b = a

c)

b = 2a

d)

b = 4a

23.

A ball thrown by one player reaches the other in 2 sec. The maximum height attained by the ball above the point of projection will be about:

a)

10 m

b)

7.5 m

c)

5 m

d)

2.5 m

24.

The maximum horizontal range of a projectile is 400 m. The maximum height attained by it will be:

a)

100 m

b)

200 m

c)

400 m

d)

800 m

25.

Two bodies are projected with the same velocity. If one is projected at an angle of 30º and the other at an angle of 60º to the horizontal, the ratio of the maximum heights reached is:

a)

3 : 1

b)

1 : 3

c)

1 : 2

d)

2 : 1

26.

A ball is projected upwards from the top of the tower with a velocity of 50 ms^–1 making an angle of 30º with the horizontal. The height of the tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground?

a)

2.33 sec

b)

5.33 sec

c)

6.33 sec

d)

9.33 sec

27.

If for a given angle of projection, the horizontal range is doubled, the time of flight becomes:

a)

4 times

b)

2 times

c)

$\sqrt[]{2}$ times

d)

1/ $\sqrt[]{2}$ times

28.

A particle is thrown with velocity u at an angle α from the horizontal. Another particle is thrown with the same

velocity at an angle α from the vertical. The ratio of times of flight of two particles will be:

a)

tan 2 α : 1

b)

cot 2 α : 1

c)

tan α : 1

d)

cot α : 1

29.

Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long–jump event?

a)

Speed before he jumps and his weight

b)

The direction in which he leaps and the initial speed

c)

The force with which he pushes the ground and his speed

d)

The direction in which he leaps and the weight

30.

For a projectile, the ratio of maximum height reached to the square of flight time is: (g = 10 ms ^–2)

a)

5 : 4

b)

5 : 2

c)

5 : 1

d)

10 : 1

31.

A cricketer can throw a ball to a maximum horizontal distance of 100 m. The speed with which he throws the ball is: (to the nearest integer)

a)

30 ms^-1

b)

42 ms^-1

c)

32 ms^-1

d)

35 ms^-1

32.

If two bodies are projected at 30º and 60º respectively, with the same velocity, then:

a)

Their ranges are same

b)

Their heights are same

c)

Their times of flight are same

d)

All of these

33.

A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth’s surface will be:

a)

$\sqrt[]{2gh+u^2}:u$

b)

1 : 2

c)

1 : 1

d)

$\sqrt[]{2gh+u^2}:\sqrt[]{2gh}$

34.

A staircase contains three steps each 10 cm high and 20 cm wide. What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane?

a)

0.5 m/s

b)

1 m/s

c)

2 m/s

d)

4 m/s

35.

An aeroplane is flying at a height of 1960 m in horizontal direction with a velocity of 360 km/hr. When it is vertically above the point. A on the ground, it drops a bomb. The bomb strikes a point B on the ground, then the time taken by the bomb to reach the ground is:

a)

$20\sqrt[]{2\ }\sec$

b)

20 sec

c)

$10\sqrt[]{2}\sec$

d)

10 sec

36.

A bomb is dropped on an enemy post by an airplane flying with a horizontal velocity of 60 km/hr and at a height of 490 m. How far the airplane must be from the enemy post at time of dropping the bomb, so that it may directly hit the target: (g = 9.8 m/s ² )

a)

$\frac{100}{3}$ m

b)

$\frac{500}{3}\ m$

c)

$\frac{200}{3}\ m$

d)

$\frac{400}{3}\ m$

37.

A body is thrown horizontally with velocity $\sqrt[]{2gh}$ from the top of a tower of height h. It strikes the level ground through the foot of tower at a distance x from the tower. The value of x is:

a)

h

b)

2h

c)

$\frac{h}{2}$

d)

$\frac{2h}{3}$

38.

The barrel of a gun and the target are at the same height. As soon as the gun is fired, the target is also released. In which of the following cases, the bullet will not strike the target

a)

Range of projectile is less than the initial distance between the gun and the target

b)

Range of projectile is more than the initial distance between the gun and the target

c)

Range of projectile is equal to the initial distance between the gun and target

d)

Bullet will always strike the target

39.

A body is projected horizontally from the top of a tower with initial velocity 18 ms ^–1. It hits the ground at angle 45º. What is the vertical component of velocity when it strikes the ground?

a)

9 ms^-1

b)

$9\sqrt[]{2}$ ms^-1

c)

18ms^-1

d)

$18\sqrt[]{2}$ ms^-1

40.

For a given velocity of projection from a point on the inclined plane, the maximum range down the plane is three times the maximum range up the incline. Then, the angle of inclination of the inclined plane is:

a)

30º

b)

45º

c)

60º

d)

90º

41.

A shell is fired from a gun from the bottom of a hill along its slope. The slope of the hill is α = 30º, and the angle of the barrel to the horizontal β = 60º. The initial velocity v of the shell is 21 m/sec. Then distance of point from the gun at which shell will fall:

a)

10 m

b)

20 m

c)

30 m

d)

40 m

42.

The maximum range of rifle bullet on the horizontal ground is 6 km its maximum range on an inclined of 30º will be

a)

1 km

b)

2 km

c)

4 km

d)

6 km

43.

A ball is projected with velocity Vo at an angle of elevation 30°. Mark the correct statement

a)

Kinetic energy will be zero at the highest point of the trajectory

b)

Vertical component of momentum will be conserved

c)

Horizontal component of momentum will be conserved

d)

Gravitational potential energy will be minimum at the highest point of the trajectory

44.

A cricketer can throw a ball to a maximum horizontal distance of 100 m. The speed with which he throws the ball is (to the nearest integer)

a)

30 ms ^–1

b)

42 ms ^–1

c)

32 ms ^–1

d)

35 ms^–1

45.

Position of a particle in a rectangular-co-ordinate system is (3, 2, 5). Then its position vector will be

a)

$3iˆ+5jˆ+2kˆ$

b)

$3iˆ+2jˆ+5kˆ$

c)

$5kˆ+3jˆ+2iˆ$

d)

None of these

46.

The vector that must be added to the vector $iˆ-3jˆ+2kˆ$ and $3iˆ+6jˆ-7kˆ$ so that the resultant vector is a unit vector along the y-axis is

a)

$4iˆ+2jˆ+5kˆ$

b)

$-4iˆ-2jˆ+5kˆ$

c)

$3iˆ+4jˆ+5kˆ$

d)

Null vector

47.

The magnitude of a given vector with end points (4, – 4, 0) and (– 2, – 2, 0) must be

a)

6

b)

$5\sqrt[]{2}$

c)

$4$

d)

$2\sqrt[]{10}$

48.

Which of the following is a vector

a)

Pressure

b)

Surface tension

c)

Moment of inertia

d)

None of these

49.

A force of 5 N acts on a particle along a direction making an angle of 60° with vertical. Its vertical component be

a)

10 N

b)

3 N

c)

4 N

d)

2.5 N

50.

A vector is represented by $3iˆ+jˆ+2kˆ$ Its length in XY plane is

a)

2

b)

14

c)

10

d)

5

Vector Motion In Straight Line Projectile Motion

Total questions: 50

Worksheet time: 25mins

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