For a maximum horizontal range of a projectile, the angle of projection should be 

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  1. 30°
  2. 45°
  3. 60°
  4. 75°

Answer (Detailed Solution Below)

Option 2 : 45°
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CONCEPT:

  • Projectile motion: The horizontal component of velocity (u cosθ )acceleration (g), and mechanical energy remain a constant while, speedvelocity, the vertical component of velocity (u sinθ)momentum, kinetic energy, and potential energy all changes.
  • Velocity and KE are maximum at the point of projection while minimum (but not zero) at the highest point.

F1 P.Y Madhu 13.04.20 D5

  • Horizontal range (R): It is the horizontal distance travelled by a body during the time of flight.

EXPLANATION:

F1 P.Y Madhu 13.04.20 D6

  • The mathematical expression of the horizontal range is given by:

Horizontal range, \(R = \frac{{u^2\sin 2θ }}{g}\)

For maximum horizontal range:

⇒ Sin 2θ = 1

⇒ 2θ = sin-1(1)

⇒ 2θ = 90°

⇒ θ = 45°
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