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**Introductory Exercise 4.2**

**Ques 1: A particle is projected along an inclined plane as shown in figure. What is the speed of the particle when it collides at point A? (g = 10 m/s ^{2})**

Using, v = u + at

v

**Ques 3: Two particles A and B are projected simultaneously from the two towers of height 10 m and 20 m respectively. Particle A is projected with an initial speed of 10âˆš2 m/s at an angle of 45Â° with horizontal, while particle B is projected horizontally with speed 10 m/s. If they collide in air, what is the distance d between the towers?****Ans: **20 m**Sol:** Let the particle collide at time t.

x_{1} = (u cos Î¸) t

and x_{2} = vt

âˆ´ d = x_{2} - x_{1}

= (v + u cos Î¸) t

For vertical motion of particle 1:

i.e., â€¦(i)

or

For the vertical motion of particle 2:

i.e., â€¦(ii)

Comparing Eqs. (i) and (ii),

â‡’ t = 1 s

âˆ´ d = 20 m**Ques 4: Two particles A and B are projected from ground towards each other with speeds 10 m/s and 5âˆš2 m/s at angles 30Â° and 45Â° with horizontal from two points separated by a distance of 15 m. Will they collide or not?****Ans: **No**Sol: **u = 10 m/s

v = 5âˆš2 m/s

Î¸ = 30Â°

Ï† = 45Â°

d = 15 m

Let the particles meet (or are in the same vertical time t).

âˆ´ d = (u cos Î¸) t + (v cos Ï†) t

â‡’ 15 = (10 cos 30Â° + 5âˆš2 cos 45Â°) t

or

or

= 1.009 s

Now, let us find time of flight of A and B

= 1 s

As T_{A} < t, particle A will touch ground before the expected time t of collision.

âˆ´ Ans: NO.**Ques 5: A particle is projected from the bottom of an inclined plane of inclination 30Â°. At what angle Î± (from the horizontal) should the particle be projected to get the maximum range on the inclined plane.****Ans: **60Â°**Sol: **For range to be maximum**Ques 6: A particle is projected from the bottom of an inclined plane of inclination 30Â° with velocity of 40 m/s at an angle of 60Â° with horizontal. Find the speed of the particle when its velocity vector is parallel to the plane. Take g = 10 m/s ^{2}.**

âˆ´ Ï† = Î²

v

v

or u cos Î± = v cos Î²

â‡’

= Vertical displacement of B

i.e., v

âˆ´ Î¸ = 30Â°

(b) x = (v

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