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

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.