## Pradeep Kshetrapal is teaching live on Unacademy Plus

PHYSICS Pradeep Kshetrapal Class XI

Chapter 4 Motion in a plain Projectile Motion Lesson No.Phy-XI-4-8

Horizontal Projectile When we throw an object from a height it will fall down travelling some horizontal distance This is known as horizontal projectile Gravity-free Path Projectile k'i Motion Yertical Motion 0n19 Range

This projectile we get because of moment of inertia of motion the initial velocity which the object has before dropping Initially the object only has horizontal velocity. Initially the vertical velocity is zero -o--o--+-+ Gravity-free Path ~ Projectile Motion Yertical Motion Only

After 1 second the vertical velocity becomes 9.8 after 2 sec the vertical velocity becomes 2x 9.8 and so on 3-o--o-+-+- o- Gravity-free Path Projectile Motion Yertical Motion Only

After hitting the ground the object will have a horizontal velocity same as initial horizontal velocity. The resultant velocity is v- ux2 + v^2 x-20m/s Vx-20m/s Vx- 20m/s vy=-19.6 m/s x-20m/s 20 m/s vy 392 m/s

Time taken to reach the ground from height h We know that, for finding time we use vertical distance formula. We are given with distance -h Acceleration a-g Initial vertical velocity 0 Time

2 2h Range : the horizontal distance covered during the projectile motion . 2h .

At time t if we need to find velocity then, Velocity at time t.

7 The direction of velocity is tan a . is the angle made by the direction of velocity with horizontal. Horizontal Velocity V Velocity on , Vertical Velocitystriking the ground

We are going to study equations of projectile. ucos e An object which is in projectile motion, at every instant its x and y co-ordinate is varying

There is a relation between x and y co-ordinate of projectile motion. This relation is expressed as an equation which is known as equation of projectile Every point of the projectile will follow this equation The utility of this equation is by x- co-ordinate we can find y- co-ordinate easily.

In case of vertical or y- direction there is always a change in velocity because of gravitational acceleration so, here distance s is expressed as s- ut +at2. y-usin +-(-g) t2 2 Since, time is the quantity which connects the two quantities in x and y- direction

The utility of this equation is if at any point of time if x is known to us we can find y and vice versa, where rest of the quantities are give to us. y- ax+ bx2 shows that the path is parabolic.

The vertical velocity is given by vv So, at time t the velocity becomes Using v- u+ at in vertical motion vy-usin 0- gt u sin 0 - gt)2

2+2 Velocity at time t depends upon initial velocity u, angle and time t. A projectile has minimum velocity at the top. Magnitude-lvl-ucos . Direction is horizontal

Direction of projectile t time t. u sin _gt 11 cos tan =- .