JEE/NEET Lec_93: I Projectile Motion on an Inclined Plane I

OPsAcademy #NEET #JEEMains #Board_Exam #Kinematics's #MotionInPlane #Projectile_Motion
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**Projectile from Heights (Throw Horizontally)
**Projectile from Heights (Projected upward at angle ø)
**Projectile from Heights (Projected downward at angle ø)


**Motion in Plane
**Analysis of Uniform Motion in Plane
Projectile Motion
**Analysis of Projectile Motion
**Equation Derive from Projectile Motion
If a particle is free to move in a plane, its position can be located with two coordinates. Motion in a plane is also referred to as a motion in two dimensions. For example, circular motion, projectile motion etc.
********************Projectile Motion*******************
When a particle is thrown obliquely near the earth's surface, it moves along a curved path. Such a particle is called a projectile and its motion is called projectile motion.
**Exam:1- The x and y coordinates of the particle at any time are x = 5t – 2t2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is? [NEET 2017]
ques-2 A body 3kg move in xy plane under the action of force given by 6t i + 4t j . Assuming that the body is at rest at time t=0 the velocity of the body is at t=3s ? [PMT 2002]
Ques-3 The position vector of a particle is r = (a cos wt) i + (a sin wt) j. Find the velocity of the particle. [PMT 2002]
Ques-4 A Bullet is fired with a speed of 1000 metre per second in order to hit a target that is 100 M away. if g equals to 10m/s^2, the gun should be aimed ? [PMT 1995]
Ques-5 A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. [PMT-2014]
Ques-6 The velocity of the projectile at the initial point is (2i+3j) m/s its velocity in m/s at point B is ? [PMT 1995]
~~~~~~~~~~~MOTION IN A STRAIGHT LINE~~~~~~~
When a particle is constrained to move on a straight line, the description becomes fairly simple.
**Note: If the velocity and the acceleration are both positive, the speed increases. If both of them are negative then also the speed increases but if they have opposite signs, the speed decreases.
~~~~~~~~~~~~UNIFORM MOTION~~~~~~~~~~~~~~
A particle is said to be in uniform motion if it covers equal displacements in equal intervals of time, however small these intervals may be.
**Key Point Uniform Motion:
*Uniform motion is a straight line motion with constant velocity.
*In uniform motion displacement and distance are equal
*The average and instantaneous velocities have same values in uniform motion.
*No net force is required for an object to be in uniform motion.
*The velocity in uniform motion does not depend upon the time interval.
*The velocity in uniform motion is independent of choice of origin
**Acceleration
It is the rate of change of velocity with respect to time and the motion of an object is said to be accelerated motion if its velocity changes with time.
**Acceleration is also defined as second time derivative of position
**Acceleration is a vector quantity. It can be positive, zero or negative
**Negative acceleration is also known as retardation or deceleration. Deceleration and acceleration have opposite directions.
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