Assertion : In projectile motion if time of flight is 4 s. Then,...

Assertion and Reason Analysis - Assertion: The assertion states that if the time of flight ($T$) is 4 s, the maximum height ($H$) is 20 m. We can verify this using the relationship between maximum height and time of flight. The time to reach the maximum height is half the total time of flight, so (t_{\text{ascent }}=T / 2= 4 / 2=2 \mathrm{ s}). Using the equation for displacement under constant acceleration: (H=u t_{\text{ascent }}+\frac{1}{2} a t_{\text{ascent }^2) The initial vertical velocity component is (u_y=g \times t_{\text{ascent }}=10 \mathrm{ m} / \mathrm{s}^2 \times 2 \mathrm{ s}=20 \mathrm{ m} / \mathrm{s}). Substituting the values: (H=(20)(2)+\frac{1}{2}(-10)(2)^2=40-20=20 \mathrm{ m} .) Alternatively, using the relationship (H=\frac{g T^2}{8}) : (H=\frac{(10)(4)^2}{8}=\frac{10 \times 16}{8}=\frac{160}{8}=20 \mathrm{ m} .) The assertion is true. - Reason: The reason claims that the maximum height is (H=\frac{g T}{2}). This formula is incorrect. As shown in the assertion analysis, the correct formula is (H=\frac{g T^2}{8}). Therefore, the reason is false. Conclusion The assertion is true, but the reason is false. This corresponds to option (3).