A projectile m = 50kg, flying at a speed of v = 800 m / s at an angle of a = 30 degrees to the vertical

| June 24, 2021 | education

A projectile m = 50kg, flying at a speed of v = 800 m / s at an angle of a = 30 degrees to the vertical, hits the platform with sand and gets stuck in it. Find the speed of the platform after being hit by a projectile if its mass is C = 16 tons.

mc = 50 kg.

Vc = 800 m / s.

∠α = 30 °.

mp = 16 t = 16000 kg.

Vп “-?

Since the projectile interacts only with a platform with sand, this system can be considered closed.

For a closed-loop system, the momentum conservation law is valid: the sum of the impulses of a closed-loop system does not change.

mс * Vсн = (mп + mс) * Vп “- vector.

mс * Vсн * cosα = (mп + mс) * Vп “- for projections on the horizontal axis.

Vp “= mc * Vsn * cosα / (mp + mc).

Vp “= 50 kg * 800 m / s * cos30 ° / (16000 kg + 50 kg) = 2.2 m / s.

Answer: after being hit by a projectile, the platform with sand will move at a speed of Vp “= 2.2 m / s.



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