Projectile motion 1
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Projectile motion is the motion of an object under the influence of gravity. It can be broken down into two components: horizontal motion and vertical motion. Horizontal motion is unaffected by gravity and follows the regular kinematic equations of straight line motion. Vertical motion is affected by the downward acceleration due to gravity and also follows straight line kinematic equations using the acceleration due to gravity. Understanding projectile motion requires analyzing the horizontal and vertical components separately using the appropriate kinematic equations for each direction.
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A projectile is an object moving under the influence of gravity with a parabolic path. Its motion can be analyzed by separating the horizontal and vertical components. In the horizontal direction, the velocity is constant, while in the vertical direction there is a constant acceleration due to gravity. Projectile motion is used to model many real-world scenarios like thrown objects, diving, and artillery fire. Solving projectile motion problems involves separating the horizontal and vertical motions and using kinematic equations with the initial velocities and gravitational acceleration.
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Projectile motion 1
- 2. What is Projectile motion? Projectile motion is the type of motion of an object under the force of gravity Example: Throwing a ball in the air at any angle the ball follows a projectile motion The image shows projectile motion as followed by a ball The path of projectile motion is a parabola 2 2 8 1 9 6 3 4 5 7
- 3. Breaking up projectile motion Important : Projectile motion is just a combination of motion in 2 directions at the same time Motion in Horizontal direction (X-direction) Motion in Vertical direction (Y-direction) When the above two motions occur at the same time, it is called PROJECTILE MOTION To understand and solve projectile motion problems, it is useful to break it up into separate horizontal and vertical components 3
- 4. Motion in Horizontal direction (X- direction) Motion in horizontal or x-direction is just straight line motion, hence we do not need to consider any vertical component or vertical motion We do not have any horizontal acceleration, only velocity is present in horizontal direction in case of projectile motion Formula to use: Velocity (in x-direction) = Distance/Time 4
- 5. Motion in Vertical direction (Y-direction) Motion in vertical or y-direction is also a straight line motion, hence we do not need to consider any horizontal component or horizontal motion Acceleration due to gravity (g=9.8m/s2) is present in the vertical direction directed downwards (towards the earth) Newton’s equations of motion (for motion under acceleration) are required: Important Equations (Remember / Memorise) v = u + a*t …1 s = u*t+(1/2)*a*t2 …2 v2 = u2 + 2*a*h …3 Here, s – distance covered; u – initial velocity; v – final velocity t – time duration of the motion; a – acceleration acting on the object; 5
- 6. Sign Convention and Directions For Horizontal Motion If motion is to the right (+ve x-direction), velocity is considered +ve If motion is to the left (-ve x-direction), velocity is considered –ve For Vertical Motion The direction of velocity and acceleration are completely independent of each other. Direction of acceleration is where the object is being pulled (or pushed) Example: downward (-ve) acceleration in case of acceleration due to gravity, hence a = -9.8m/s2, as the object is pulled downward due to gravity 6
- 7. End of Part-1 Coming up: Other useful results Numerical Examples. 7