A projectile is thrown from a point O on the ground at an angle 45^ from the vertical and with a speed 5 2 ~m / s . The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 ~s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity g=10 ~m / s ^ 2 . The value of t is _________.
A. A
After splitting of projectile in two equal parts one part falls vertically down to the ground. So, velocity of another part will be according to conservation of linear momentum, m × 5 = m 2 × 0 + m 2 × v ⇒ v = 10   m   s − 1 Now time taken by m 1 , to reach ground, since after splitting of projectile m 1 will perform horizontal projectile so, t = 2 h g ⇒ t = 2 u 2 sin 2 θ 2 g 2 ⇒ t = 2 × 50 2 × 10 × 10 × 1 2 = 0.25 ⇒ t = 0.5   s
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