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]

Question

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],

MARKS App · Accepted Answer

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 ⁡ 75 o g The man is in danger for a time T 2 - T 1 = 2 u g sin ⁡ 75 o - sin ⁡ 15 o = 2 u g 2 cos ⁡ 45 o sin ⁡ 30 o u s i n g i d e n t i t y , sin ⁡ C - sin ⁡ D = 2 cos ⁡ C + D 2 sin ⁡ C - D 2 = 2 × 60 10 × 2 × 1 2 × 1 2 = 72 s

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