# motion in a plane class 11 numericals with solutions

*Dear students in this page contains **motion in a plane class 11 numericals with solutions pdf. It also contains pdf for neet questions of chapter 3 motion in a straight line class 11 jee questions, aiims important questions at one place to get you all prepared for your neet, aiims ,jee main, advance exams as well as cbse board exams and other board exams. Visit my nawendu classes youtube channel for more help.*

1. A particle starting from the origin (0,0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are $(\sqrt{3},3)$ .The path of the particle makes with the X-axis an angle of

CBSE PMT 2007

Answer- 60 degree

2. The coordinates of moving particle at any time t are given by $x=\alpha {{t}^{3}}$ and $y=\beta {{t}^{3}}$ .The speed of the particle at time t is given by

AIEEE 2003

Answer- $3{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}$

3. The x and y coordinates of the particle at any time are \[x=5t-2{{t}^{2}}\] and y=10t respectively ,where x and y are in meters and t in seconds. The acceleration of the particle at t=2 sec is

NEET 2017

Answer- $-4m/{{s}^{2}}$

4. Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the right is 10m/s. What is the velocity of B when angle $\alpha ={{60}^{\circ }}$ ?

CBSE AIPMT 1998

Answer- 17.3 m/s

5. Two balls are thrown simultaneously from ground with same velocity of 10 m/s but different angles of projection with horizontal. Both balls fall at same distance $5\sqrt{3}$m from point of projection . What is the time interval between the balls striking the ground ?

Answer- $\sqrt{3}-1$ second

6. A particle is moving such that its position co-ordinates (x,y) are (2m,3m) at time t=0 s ,(6m,7m) at time t=2 s ,and (13m,14m) at time t=5 s

Average velocity of vector (${{\vec{v}}_{av}}$) from t=0s to t=5s is

CBSE AIPMT 2014

Answer- $\frac{11}{5}(\hat{i}+\hat{j})$

7. Two projectile A and B thrown with speeds in the ratio $1:\sqrt{2}$ acquires the same heights. If A is thrown at an angle of ${{45}^{\circ }}$with the horizontal , the angle of projection of B will be

KERALA CEE 2011

Answer- ${{30}^{\circ }}$

8. A boy can throw a stone up to a maximum height of 10m.The maximum horizontal distance that the boy can throw the same stone up to will be

IIT JEE MAIN 2013

Answer- 20 m

9. An aero plane is moving with a horizontal velocity u at a height h. The velocity of a packet dropped from it on the earth surface will be

AFMC 1999

Answer- \[{{({{u}^{2}}+2gh)}^{1/2}}\]

10. A missile moves is fired for maximum range with initial velocity 20 m/s. If g= 10 $m/{{s}^{2}}$ ,the range of missile is

CBSE PMT 2011

Answer- 40m

11. A particle of mass m is projected with velocity v making an angle of 45 degree with horizontal direction .When particle lands on level ground the magnitude of change in its momentum will be

CBSE PMT 2008

Answer- $mv\sqrt{2}$

12. A ball whose kinetic energy is E, is thrown at an angle of 45 degree with the horizontal. It’s kinetic energy at the highest point of its flight will be

CBSE PMT 1997

Answer- E/2

13. A ball whose kinetic energy is E, projected at an angle \[{{60}^{\circ }}\] to horizontal .The kinetic energy of the ball at the highest point of its flight will be

AIEEE 2002

Answer- E/4

14. A projectile is fired at an angle of ${{45}^{\circ }}$ with the horizontal .Elevation angle of the projectile at its highest point as seen from the point of projection is

CBSE PMT 2011

Answer- ${{\tan }^{-1}}(\frac{1}{2})$

15. A bullet is fired from a gun with speed of 1000 m/s in order to fit a target 100m away. At what height above the target should the gun be aimed ?(resistance of air is negligible and g=10 $m/{{s}^{2}}$)

CBSE PMT 1995

Answer- 5 cm

16. The speed of a boat is 5km/h in still water. If it crosses river of width 1 km along the shortest possible path in 15 minutes, the velocity of the river’s water is

CBSE PMT 2000

Answer- 3km/h

17. A person swims in river aiming to reach exactly opposite point on the bank of river . His speed of swimming is 0.5 m/s at an angle 120 degree with the direction of flow of water. The speed of water in stream is

CBSE 1999

Answer- 0.25 m/s

18. A boat is sent across a river with velocity of 8 km/h .If the resultant velocity of boat is 10 km/h, then the velocity of the river is

CBSE PMT 1993 , AIIMS 2016

Answer- 6 km /h

19. The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?

IIT 2019 MAIN ,9 APRIL I

Answer - ${{120}^{\circ }}$

20. Rain is falling vertically downwards with a velocity of 3 km/h. A man walks in the rain with a velocity of 4 km/h. The rain drop will fall on the man with a velocity

AIIMS 1997

Answer- 5 km /h

21. A projectile is thrown in upward direction making an angle of \[{{60}^{\circ }}\] with horizontal direction with a velocity of 147 m/s. Then the time after which its inclination with the horizontal is \[{{45}^{\circ }}\]

AFMC 2006

Answer- 5.49 s

22. A stone is tied to the end of a string of 1m long is whirled in a horizontal circle with a constant speed. If the stone make 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone ?

CBSE PMT 2005

Answer- ${{\pi }^{2}}m/{{s}^{2}}$ toward center

23. An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rev/min, acceleration of a point on the tip of the blade is

CBSE AIPMT 1990

Answer- 47.4$m{{s}^{-2}}$

24. P is the point of contact of a wheel and the ground. The radius of wheel is 1m. The wheel rolls on the ground without slipping. The displacement of point P when wheel completes half rotation is

CBSE AIPMT 2002

Answer- $\sqrt{{{\pi }^{2}}+4}$ m

25. A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 rad/s. What is its linear velocity at a point on circular path ?

CBSE AIPMT 1996

Answer- 2m/s

26. Two balls are thrown horizontally from the top of a tower with velocities ${{v}_{1}}$ and ${{v}_{2}}$ in opposite directions at the same time . After how much time , the angle between velocities of balls becomes ${{90}^{\circ }}$ ?

AIIMS 2016

Answer- $\frac{\sqrt{{{v}_{1}}{{v}_{2}}}}{g}$

27. A balloon rises from the rest with a constant acceleration g/8. A stone is released from it when it has risen to height h . The time taken by the stone to reach the ground is

AIIMS 2010

Answer- $2\sqrt{\frac{h}{g}}$

28. The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s-1 can go without hitting the ceiling of the hall ?

Answer- 150.5 m

29. A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball ?

Answer- 50 m

30. The position of a particle is given by \[\vec{r}=3t\hat{i}-2{{t}^{2}}\hat{j}+4\hat{k}m\] where t is in seconds and the coefficients have the proper units for r to be in metres.

(a) Find the v and a of the particle?

(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

Answer- (a)\[\vec{v}\left( t \right)=3\hat{i}-4t\hat{j},\vec{a}\left( t \right)=-4\hat{j}\]

(b) 8.54 m/s, 70° with x-axis.

31. The position vector of a particle changes with time according to the relation $\vec{r}=15{{t}^{2}}\hat{i}+(4-20{{t}^{2}})\hat{j}$ . What is the magnitude of acceleration (in $m/{{s}^{2}}$ ) at t=1 ?

IIT 2019 MAIN ,,9 APRIL II

Answer- 50

32. A particle starts from the origin at t = 0 s with a
velocity of 10

(a) At what time is the x- coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?

(b) What is the speed of the particle at the time ?

Answer-(a) 2 s, 24 m, (b) 21.26 m/s

33. An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the speed of the aircraft ?

Answer- 182 m/s

34. A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away ? Assume the muzzle speed to be fixed, and neglect air resistance.

Answer- No

35. A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s-1 to hit the plane ? At what minimum altitude should the pilot fly the plane to avoid being hit ? (Take g = 10 m s-2 ).

Answer- At an angle of ${{\sin }^{-1}}\left( \frac{1}{3} \right)={{19.5}^{\circ }}$ with the vertical; 16 km

36. A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?

Answer- 0.86 $m/{{s}^{2}}$, ${{54.5}^{\circ }}$ with the direction of velocity

37. In the given figure , a= 15 $m/{{s}^{2}}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R= 2.5 m at a given instant of time .The speed of the particle is

NEET 2016

Answer- 5.7 m/s

38. (a) Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by $\theta (t)={{\tan }^{-}}\left( \frac{{{v}_{oy}}-gt}{{{v}_{oy}}} \right)$

(b) Shows that the projection angle θ0 for a projectile launched from the origin is given by

${{\theta
}_{0}}={{\tan }^{-1}}\frac{4{{h}_{m}}}{R}$

where the symbols have their usual meaning.

39. A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If ${{t}_{1}}$ and ${{t}_{2}}$ are the values of the time taken by it to hit the target in two possible ways ,the product ${{t}_{1}}{{t}_{2}}$ is

IIT 2019 MAIN , 12 APRIL II

Answer- $\frac{2R}{g}$

40. A projectile is given an initial velocity of (\[\hat{i}+2\hat{j}\] )m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If g= 10 $m/{{s}^{2}}$, then equation of trajectory is

IIT 2013 MAIN

Answer- $y=2x-5{{x}^{2}}$

41. A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in the figure .The horizontal velocity of the block is

AIIMS 2017

Answer- \[\frac{v}{\sin \theta }\]

42. In the arrangement shown in the figure , the ends P and Q of an
unstretchable string move downwards with uniform speed U. Pulleys A and B are
fixed. Mass M moves upward with a speed

IIT 1982

Answer- $\frac{U}{\cos \theta }$

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