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Physics Smart Booklet 1 4.MOTION IN A PLANE Physics Smart Booklet Theory + NCERT MCQs + Topic Wise Practice MCQs + NEET PYQs
Physics Smart Booklet 2
Physics Smart Booklet 3 MOTION IN A PLANE Motion with uniform acceleration in a plane Consider a point object moving in XY plane with an uniform acceleration a . Let us suppose ‘O’ be the origin for measuring time and position of the object. Let the object be at positions A and B at times t1 and t2 respectively, where OA r and OB r = = 1 2 . Let v and v 1 2 be the velocities of object at instants t1 and t2 respectively, then constant acceleration is given by 2 1 2 1 v v a t t − = − v v a(t t ) 2 1 2 1 − = − v v a(t t ) 2 1 2 1 = + − If t1 = 0, t2 = t, v u and v v 1 2 = = then v u at = + The above equation can be expressed in terms of rectangular components in XY plane as follows. x y ˆ ˆ u u i u j = + where 2 2 x y u u u = + x y ˆ ˆ v v i v j = + where 2 2 x y v v v = + x y ˆ ˆ a a i a j = + where 2 2 x y a a a = + Also, vx = ux + axt and vy = uy + ayt Displacement in x-direction is given by 2 0 x x 1 x x u t a t 2 − = + And displacement in y-direction is given by 2 0 y y 1 y y u t a t 2 − = + ▪ Projectile Projectile is the name given to a body thrown with some initial velocity making an angle  [ 90] with the horizontal direction, and then allowed to move in two dimensions under the action of gravity alone, without being propelled by any engine or fuel. y A B x O
Physics Smart Booklet 4 The path followed by a projectile is called its ‘trajectory’. Examples of projectile are: (i) A ball hit by a bat (ii) A bullet fired from a gun or pistol (iii) A javelin thrown by an athlete (iv) A shot-put sphere thrown by an athlete (v) A body dropped from an aeroplane in flight / bus / train In the above examples, we find that a projectile moves under the combined effect of two velocities: 1. A uniform velocity in the horizontal direction, which would not change provided there is no air resistance. 2. A uniformly changing velocity in the vertical direction due to gravity. To study the motion of a projectile, the following assumptions are made. (i) There is no resistance of air. (ii) The effect due to rotation of earth and curvature of the earth is neglected. (iii) The acceleration due to gravity (g) is constant in magnitude and in direction at all points of the motion of projectile. ▪ Horizontal Projectile When a body is projected horizontally with a velocity from a point above the ground level, it is called a “horizontal projectile”. When a stone is projected horizontally with a velocity ‘u’ from the top of a tower of height ‘h’ it describes a parabolic path as shown in figure. (i) Time of descent, 2h t g = (independent of ‘u’) (ii) Horizontal displacement (or) range is 2h R u g = (iii) The speed with which it hits the ground is 2 2 2 2 v u 2gh u g t = + = + (iv) The angle at which it strikes the ground is 1 1 gt 2gh tan tan u u − −      = =           u h R   u v gt Parabolic path