IMPACT

IIT-JEE, 2013projectile motion Time: 1 Hours Maximum Mark: 74

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IMPACT - I.D.: FORMCHECKBOX

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A. Question paper format:1. The question paper consists of 1 part (Physics). 2. Section A contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is correct.

3. Section B contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which one or more is/are correct.

4. Section C contains 2 groups of questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is correct.5. Section D contains 2 questions. Each question has four statements (A, B, C and D) given in column I and four statements (p, q, r and s) in Column II. Any given statement in column I can have correct matching with one or more statements(s) given in column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B, darken the bubbles corresponding to q and r in the ORS.

Projectile MotionSection-ASingle Correct answer typeThis section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct

Marking Scheme (+ 3, 1)1. The equation of projectile is . Its horizontal ranges is

a) pqb) p/qc) pd) q

2.A large number of bullets are fired in all directions with the same speed V. What is the maximum area on the ground on which these bullets will spread?

a)

b)

c)

d)

3.A particle has an initial velocity of and an acceleration of . Its speed after 10s is

a) 10 unitsb) 8.5 unitsc) unitsd) 7 units

4.Two paper screens A and B are separated by a distance of 200m. A bullet pierces A and then B. The hole in B is 40cm below the hole in A. If the bullet is traveling horizontally at the time of hitting A, then the velocity of the bullet at A is

a) 200 m/sb) 400 m/sc) 600 m/sd) 700 m/s

5.A particle starts form the origin of coordinates at time t = 0 and moves in the x-y plane with a constant acceleration in the y direction. Its equation of motion is . Its velocity component in the x-direction is

a)

b)

c)

d) Variable

6.The taken by the projectile to reach form A to B is t, then the distance AB is equal to

a)

b)

c)

d)

7.From an inclined plane two particles are projected with same speed at same angle , one up and other down the plane as shown in figure. Which of the following statements (s) is /are correct?

a) The time of flight of each particle is the same

b) The particles will collide the plane with same speed

c) Both the particles strike the plane perpendicular

d) The particles will collide in mid air if projected simultaneously and time of flight of each

particle is less than the time of collision

8.A particle moves in the x y plane with velocity . If it passes through the point x = 14 at t = 2s, then the equation of the path is

a)

b) c)

d)

Section-BMultiple Answer Correct typeThis section contains 4 multiple choice questions numbered 9 to 12. Each question has 4 choices (A), (B), (C) and (D), out of which may have ONE or MORE THAN ONE is correct

Marking Scheme (+4, 0)9.A ball is dropped onto a pad at O and rebounds with a velocity u at an angle 600 with the horizontal as shown in Figure. The ball will enter the window W of width 0.5m at a height 1m, if u is

a) 50 m/sb) 10 m/sc) 6 m/sd) 5 m/s

10.The path of a particle moving under the influence of a force fixed in magnitude and direction is

a) Straight line b) Circle c) Parabolad) Ellipse

11.Two projectiles are fired form the same point with the same speed at angle of projection 600 and 300 respectively. Which one of the following is true?

a) Their maximum height will be the sameb) Their range will be the same

c) Their landing speed will be the samed) Their time of flight will be the same

12.In case of projectile motion of two projectiles A and B are projected with the same speed at angles 150 and 750 respectively to the horizontal, then

a) HA > HB

b) HA < HB

c) TA > TB

d) TA < TB

Section-CParagraphs TypeThis section contains 2 paragraphs containing a total of 6 multiple choice questions numbered 13 to 18. Each question has 4 choice (A), (B), (C) and (D) out of which only one correct .

Marking Scheme (+ 3 1)The path of a projectile motion is given by the relation . Here x and y are in metres and g = 10 m/s2. For this projectile answer the following questions:13.What is the initial velocity of projection of the projectile

a)

b)

c)

d)

14.The initial angle of projection of the projectile is

a)

b)

c)

d)

15.The maximum height of the projectile is

a) 20 mb) 40 mc) 60 md) 80 m

PASSAG - 16 to 18:Two second after projection, a projectile is traveling in direction inclined at 300 to the horizontal. After 1 more second, it is traveling horizontally (Use g = 10ms-2).16.The time of flight of projectile is

a) 3 sb) 4 sc) 4.5 sd) 6 s

17.The initial velocity of its projection is

a) 10 m/sb) msc) 20 m/sd) ms-118.The angle of projection of the projectile is

a) 300b) 450c) 600d) None of the above

Section-DMatrix MatchThis section contains 2 questions. Each question contains statements given in two columns which have to be matched. Statements (p,q,r,s) in column-I have to be matched with statements (a,b,c,d) in Column-II. The answers to these questions have to be approximately bubbled as illustrated in the following example. If the correct matches are p-a,d q-b,c, r-a,b s-d then the correctly bubbled 4 4 matrix should be as shown.

Marking Scheme (+ 8, 0)19.The equation of motion of a projectile is y = ax bx2, where a and b are constant of motion. Match the

quantities of Column-I with the relations of Column-II

Column-I

Column-II

A) The initial velocity of projection

P)

B)The horizontal rage of projectile

Q)

C) The maximum vertical height attained by projectileR)

D) The time of flight of projectile

S)

20.Four balls of same masses are projected with the equal speeds at angles 150, 300, 600 and 750 with the horizontal direction from the ground. Match the quantities of Column-I with the angle of projection given in Column-II

Column-I

Column-II

A) Horizontal range is maximum for angle

P)

B) The vertical height is maximum for angle

Q)

C) The time of flight is minimum for angle

R)

D) The horizontal range is minimum for angle

S)

KEY1b2b3a4d5b

6d7a8b9a,b,c10a,c

11b,c12b,d13c14a15a

16d17d18c19A-p ; B-s,

C-r ; D-q20A-q,r ; B-s

C-p ; D-p,s

SOLUTIONS

1.The equation for the path of projectile during oblique projection is

..(i)

Where R is the horizontal range of projectile. From the given equation of projectile, we have

..(ii)

Comparing (i) and (ii), we have

2.If R is the max. H.R., then area covered by bullets

3.

So

4.Refer to figure

Ort = 200 / u

Also,

On solving

5.

Or

=

because the particle has acceleration along Y-direction]

As per question,

Or

6.Refer figure, horizontal component of velocity at A

7.Here,

Time of flight of A is,

Time of flight of B is,

So T1 = T2. The acceleration of both the particles is g downwards. Therefore, relative acceleration between the two is zero or relative motion between the two is uniform. The relative velocity of A w.r.t. B is towards AB, therefore collision will take place between the two in mid air.

8.Velocity along x-axis,

Or

Integrating it, we have

At

Or

(i)

Also,

Integrating it, .

At

.(ii)

In order to find the equation of path of projectile we have to eliminate t form (i) and (ii). From (ii) . Putting it in (i), we get

9.Taking horizontal motion from O to W, we have

Or

(1)

Taking vertical motion from O to W, we have

If

then

10.If the force is acting on particle in the direction of motion, the particle will describe straight line path. If the force is acting at an angle of motion of the particle, the path of a particle is parabolic path.11.Horizontal range will be the same when angle of projection is . The speed of projectile at the point of projection is equal to the speed of landing in the absence of fractional forces or viscous forces.12.When , then horizontal range is same

Maximum Height

And time of flight

i.e.

13.The trajectory of projectile motion is

14.Comparing it with the standard equation of projectile given angular projection with velocity u making an angle with the horizontal direction

i.e.

We have;

Or

And

Or

Or

15.Maximum height

16.Since after (two + one) second, the projectile is traveling horizontally, so

17.Time of flight,

Or

Vertical velocity after 2 seconds,

Horizontal velocity after 2 seconds,

As per question,

Or

18.

19.(A) Comparing the equation, with the equation of projectile motion

We have,

Or

Or

(B) Horizontal range

(C) Maximum height

(D) As,

Time of flight

20.(A) Horizontal range,

It is maximum if the value of is maximum.

It is so when

(B)Maximum vertical height

It is maximum if the value of is maximum. It is so when

(C)Time of flight

It is minimum if the value of is minimum, i.e.,

(D)Horizontal range is minimum if has minimum value

It is so if

EMBED CorelDRAW.Graphic.11

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