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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Q: 68 (NDA-II/2014)
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

question_subject: 

Maths

question_exam: 

NDA-II

stats: 

0,1,5,1,2,1,2

keywords: 

{'tall tower': [0, 0, 0, 1], 'speed': [0, 1, 2, 0], 'bullet': [0, 1, 0, 4], 'ground': [2, 1, 4, 17], 's2': [0, 1, 2, 6]}

The correct answer is option 3: 20 s.

To determine the time taken by the bullet to reach the ground, we need to calculate the time it takes for the bullet to reach its maximum height and then the time it takes to fall back down to the ground.

First, let`s calculate the time it takes for the bullet to reach its maximum height. Since the bullet is fired vertically up, its initial velocity is positive and its final velocity, when it reaches maximum height, is 0. We can use the equation:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

Here, u = 80 m/s, v = 0 m/s, and a = -10 m/s^2 (negative since the acceleration acts in the opposite direction to the initial velocity). Plugging in these values, we can solve for t:

0 = 80 - 10t

10t = 80

t = 8 s

So, it takes 8 seconds for the bullet to reach its maximum height.

Next, we need to calculate the time it takes for the bullet to fall back down to the ground. The height from which the bullet