## Saturday, March 4, 2017

### Range and Maximum height of Projectile Motion Video Lesson

Range of the projectile is the maximum horizontal distance travelled by a projectile during its time of flight. By the time the end of time of flight, the vertical displacement of the projectile is zero but its initial and final positions along the horizontal direction are different. We can find the horizontal displacement of a projectile as the product of velocity of projectile along the horizontal direction and time taken for the journey. The time taken to complete projectile motion is called time of flight. The horizontal displacement that the projectile has during the time of flight is the maximum horizontal displacement and it is called range of the projectile. We can find the range of the projectile as shown in the video lesson below.

It is found that the range of a projectile depends on the initial velocity of projection and angle of projection. So it is clear that the range of a projectile is maximum for an angle of projection 45 degree. It is the reason due to which people try to project any body with an angle close to 45 degree when they want to get maximum horizontal distance like disc and javelin throw.

Range is same for two angles of projection

It can be proved that the range of the projectile is same for complimentary angels of projection. The heights that they reach is different but the maximum horizontal range that both of them takes for complimentary angles are same. It is shown in video lectures as shown in the video below.

Maximum height of projectile

Maximum height of the projectile is the maximum vertical displacement that a projectile has during its journey. We can measure it using the equation of motion of one dimension itself. The projectile has initial velocity component along the vertical direction. As it is moving up against the gravity, its velocity keeps on decreasing and the point at which the vertical component of velocity becomes zero is called maximum direction. We can derive the equation in the video lesson as shown in the diagram below.

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