physics - motion in a plane

Class 11 - Physics

Motion in a Plane


A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km/h. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?



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Questions and Answers

Motion in a Plane - Questions

Figure shows the orientation of two vectors u and v in the TY-plane.
which of the following is correct?
(a) a and p are positive while b and q are negative
(b) a, p and b are positive while q is negative
(c) a, q and b are positive while p is negative
(d) a, b, p and q are all positive


A man wants to reach from A to the opposite comer of the square C. The sides of the square are 100 m. A central square of 50 m x 50 m is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he can walk only at a speed of v m/s (v < 1). What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?



The component of a vector r along X-axis will have maximum value if
(a) r is along positive Y-axis
(b) r is along positive X-axis
(c) r makes an angle of 45 ° with the X-axis
(d) r is along negative Y-axis


A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m/s over the hill. The canon is located at a distance of 800 m from the foot of hill and can be moved on the ground at a speed of 2 m/s, so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? Take g= 10 m/s2.


A girl riding a bicycle with a speed of 5 m/s towards north direction, observes rain falling vertically down. If she increases her speed to 10 m/s, rain appears to meet her at 45 ° to the vertical. What is the speed of the rain? In what direction does rain fall as observed by a ground based observer?


A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in figure. If he maintains constant speed of 10 ms"1, what is his acceleration at point R in magnitude and direction?



A particle is projected in air at an angle β to a surface which itself is inclined at an angle α to the horizontal (figure).
(a) Find an expression of range on the plane surface (distance on the plane from the point of projection at which particle will hit the surface).
(b) Time of flight.
(c) β at which range will be maximum



A particle falling vertically from a height hits a plane surface inclined to horizontal at an angle θ with speed v0 and rebounds elastically. Find the distance along the plane where it will hit second time.


A cricket fielder can throw the Cricket ball with a speed v0. If he throws the ball while running with speed u at an angle θ to the horizontal, find
(a) the effective angle to the horizontal at which the ball is projected in air as seen by a spectator.
(b) what will be time of flight?
(c) what is the distance (horizontal range) from the point of projection at which the ball will land?
(d) find θ at which he should throw the ball that would maximize the horizontal range as found in (c).
(e) how does θ for maximum range change if u > v0, u = v0, u < v0?
(f) how does θ in (e) compare with that for u = 0 (i.e., 45 °)?


The horizontal range of a projectile fired at an angle of 15 ° is 50 m. If it is fired with the same speed at an angle of 45 °, its range will be
(a) 60 m (b) 71m (c) 100 m (d) 141m


Which one of the following statements is true?
(a) A scalar quantity is the one that is conserved in a process.
(b) A scalar quantity is the one that can never take negative values.
(c) A scalar quantity is the one that does not vary from one point to another in space.
(d) A scalar quantity has the same value for observers with different orientation of the axes.


For a particle performing uniform circular motion, choose the correct
statement(s) from the following.
(a) Magnitude of particle velocity (speed) remains constant.
(b) Particle velocity remains directed perpendicular to radius vector.
(c) Direction of acceleration keeps changing as particle moves.
(d) Angular momentum is constant in magnitude but direction keeps changing.


A ball is thrown from a roof top at an angle
of 45 ° above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have
(a) greatest speed
(b) smallest speed
(c) greatest acceleration Explain.


The component of a vector r along X-axis will have maximum value if
(a) r is along positive Y-axis
(b) r is along positive X-axis
(c) r makes an angle of 45 ° with the X-axis
(d) r is along negative Y-axis


A particle is projected in air at some angle to the horizontal, moves along parabola as shown in figure where x and y indicate horizontal and vertical directions, respectively. Show in the diagram, direction of velocity and acceleration at points A, B and C.


When an object is dropped/released by any moving vehicle. Then initial velocity of the object is same as the moving vehicle.


A river is flowing due east with a speed 3 m/s. A swimmer can swim in still water at a speed of 4 m/s (figure).
(a) If swimmer, starts swimming due north, what will be his resultant velocity (magnitude and direction)?
(b) If he wants to start from point A on south bank –
and reach opposite point B on north bank,
(i) which direction should he swim?
(ii) what will be his resultant speed?
(c) From two different cases as mentioned in (a) and (b) above, in which case will he reach opposite bank in shorter time?


Given below in Column I are the relations between vectors a, b and c and in Column II are the orientations of a, b and c in the AY-plane. Match the relation in Column I to correct orientations in Column II.
Column I
(a) a + b = c
(b) a – c = b
(c) b – a = c
(d) a+b+c = 0

Column II


In dealing with motion of projectile in air, we ignore effect of air resistance on motion. This gives trajectory as a parabola as you have studied. What would the trajectory look like if air resistance is included? Sketch such a trajectory and explain why you have drawn it that way.


A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km/h. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?


A particle slides down a frictionless parabolic (y = x2) track (A – B – C)
starting from rest at point A (figure). Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then
(a) KE at P = KE at B
(b) height at P = height at A
(c) total energy at P = total energy at A
(d) time of travel from AtoB



Two particles are projected in air with speed v0 at angles θ1 and θ 2 (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then tick the right choices.

(a) Angle of projection: θ1 > θ2
(b) Time of flight: T1 > T2
(c) Horizontal range: Rx> R2                                    
(d) Total energy: U1> U2


A football is kicked into the air vertically upwards. What is its (a) acceleration and (b) velocity at the highest point?


A boy travelling in an open car moving on a levelled road with constant speed tosses a ball vertically up in the air and catches it back. Sketch the motion of the ball as observed by a boy standing on the footpath. Give explanation to support your diagram.


A boy throws a ball in air at 60 ° to the horizontal along a road with a speed of 10 m/s (36 km/h). Another boy sitting in a passing by car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if car has a speed of 18 km/h. Give explanation to support your diagram.


(a) Earth can be thought of as a sphere of radius 6400 km. Any object (or a person) is performing circular motion around the axis of the earth due to the earth rotation (period 1 day). What is the acceleration of object on the surface of the earth (at equator) towards its centre? What is it at latitude 9? How does these accelerations compare with g = 9.8 m/s2? (b) Earth also moves in circular orbit around the sun once every year with an orbital radius of 1.5 x 1011 What is the acceleration of the earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s2?

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