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Q67 (NDA-II/2014) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

A bullet is fired vertically up from a 400 m tall tower with a speed 80 m/s. If g is taken as 10 m/s2, the time taken by the bullet to reach the ground will be

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Your answer: —  Â·  Correct: C
Explanation

To find the time taken by the bullet to reach the ground, we use the kinematic equation for vertical motion: s = ut + (1/2)at". Defining the upward direction as positive, the initial velocity (u) is +80 m/s, the acceleration due to gravity (a) is -10 m/s", and the total displacement (s) is -400 m because the bullet ends up 400 m below its starting point. Substituting these values gives: -400 = 80t - 5t". Rearranging into a standard quadratic equation: 5t" - 80t - 400 = 0, which simplifies to t" - 16t - 80 = 0. Solving using the quadratic formula, t = [16 ± ∑(16" - 4(1)(-80))] / 2, which results in t = [16 ± ∑(256 + 320)] / 2 = [16 ± ∑576] / 2. This yields t = (16 ± 24) / 2. Since time must be positive, t = 40 / 2 = 20 seconds.

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