A shell bursts on contact with the ground and pieces from it fly in all directions with a velocity equal to 60 m s - 1 . If it is known that a man who is 180 m away is in danger for a time interval of x seconds, then what is the value of x ? [Neglect the height of the man]

Step-by-step solution

Given, u = 60  m   s - 1 ,   R = 180   m   ∴     R = u 2 g sin ⁡ 2 θ 180 = 60 2 10 sin ⁡ 2 θ ⇒   sin ⁡ 2 θ = 1 2 ⇒   θ = 15 o As there are always two directions of projections θ and 90 o - θ for the given range, hence two directions of projection, i.e. 15 o and 90 o - 15 o , i.e. 15 o and 75 o . Let T 1 and T 2 be the times of flight in the two cases, where T 1 = 2 u sin ⁡ 15 o g and T 2 = 2 u sin &#