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Question

At what angle should a projectile with initial velocity 'v' be thrown, so that it achieves its maximum range?


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Solution

Step 1: Projectile motion

  1. Projectile refers to an object that is in flight after being thrown or projected.
  2. Projectile motion is experienced by an object that moves along a curved path under the action of gravity only.

Step 2: An illustrative diagram of projectile motion

Step 3: Solution

The range of projectiles depends on the horizontal velocity and the time in flight. The flight time depends on the vertical velocity. At 45° angle both horizontal and vertical velocity are equal. From the formula of range :

R=u2Sin2θg

where, R= range, u= initial velocity, g= gravitational constant.

At θ=45° we will get Sin90° which will give us the maximum value of the range.

Hence, at 45°angle it will achieve maximum range.


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