Question

A projectile is projected with velocity of \( 40 \) m/s at an angle \( \theta \) with the horizontal. If \( R \) is the horizontal range covered by the projectile and after \( t \) seconds its inclination with horizontal becomes zero, then the value of \( \cot \theta \) is:
[Take, \( g = 10 \) m/s\( ^2 \)]

• A. \( \frac{R}{20t^2} \)
• B. \( \frac{R}{10t^2} \)
• C. \( \frac{5R}{t^2} \)
• D. \( \frac{R}{t^2} \)

Hint:

For projectile motion, the horizontal range is given by: \[ R = \frac{u^2 \sin 2\theta}{g} \] Using this formula helps in solving range-related problems quickly.