Question

A cannon fires two similar shells one after the other each with a velocity of 100 m/s at angles 60$^\circ$ and 30$^\circ$ respectively with the horizontal such that they both hit the target at the same time. The time interval between the firing of the two shells is (Acceleration due to gravity = 10 m/s²).

• A. 6.57 s
• B. 7.32 s
• C. 8.28 s
• D. 3.14 s

Hint:

The range and time of flight of a projectile depend on the angle and velocity.

Answer 1

The Correct Option is C

Step 1: Time of Flight Formula

\[ T = \frac{2 v \sin\theta}{g} \] For \( \theta_1 = 60^\circ \), \( \theta_2 = 30^\circ \), solving gives: \[ \text{Time interval} = 8.28 \text{ s} \]
Step 3: Conclusion

Thus, Option (3) is correct.