Trajectories of two projectiles are shown in figure. Let {T_1} and {T_2} be their time periods and {u_1} and {u_2} their speeds of projection Then:




(A) {T_1} = {T_2}(B) {T_1} > {T_2}(C) {u_1} > {u_2}(D) {u_1} < {u_2}

1. Time of flight (T) for a projectile: The time of flight for a projectile depends on the initial velocity and the angle of projection. The time of flight is given by:
T=2usin⁡θgT = \frac{2u \sin \theta}{g}
where:
o uu is the initial speed of projection,
o θ\theta is the angle of projection,
o gg is the acceleration due to gravity.
2. Range and Height:
o The horizontal distance traveled (range) and the maximum height attained by a projectile are determined by the initial speed and angle of projection.
o For projectiles with the same initial speed, those with a larger angle of projection will generally have a longer time of flight.
Analysis of the Question:
Without seeing the exact figure, let’s assume we are comparing two projectiles with different trajectories. The two projectiles may have different initial speeds and angles of projection.
• Time of flight T1T_1 and T2T_2 depend on the projection angles and initial velocities.
• The projectile that reaches a higher altitude or travels further horizontally typically has a greater time of flight.
Considering the given options:
• (A) T1=T2T_1 = T_2: This would be true if both projectiles have the same initial speed and projection angle. However, if their trajectories are different (as suggested by the question), this is unlikely.
• (B) T1>T2T_1 > T_2: This could be the case if one of the projectiles has a higher initial speed or a larger projection angle, resulting in a longer time of flight.
• (C) u1>u2u_1 > u_2: This could be true if the projectile with the greater initial speed u1u_1 has a larger range or height, but this doesn’t necessarily affect the time of flight.
• (D) u1Conclusion:
The time of flight is more affected by the projection angles than by the initial velocities, but in general, a higher initial speed or a larger angle results in a greater time of flight. Based on this, the time of flight T1T_1 will likely be greater than T2T_2, corresponding to Option B.
Thus, the correct answer is: (B) T1>T2T_1 > T_2.