A car with a mass of 2 tons, moving along a highway at a speed of 50 km / h, was hit by a projectile weighing 10 kg

A car with a mass of 2 tons, moving along a highway at a speed of 50 km / h, was hit by a projectile weighing 10 kg, flying perpendicular to the highway at a speed of 2780 m / s, and got stuck in it. At what angle to the highway will the car move immediately after being hit by a shell?

ma = 2 t = 2000 kg.

Vа = 50 km / h.

msn = 10 kg.

Vsn = 2780 km / h.

∠α = 90 °.

∠φ -?

When a projectile hits a car, according to the law of conservation of momentum, the projectile will tell the car the speed Vа1, perpendicular to its movement (highway).

msn * Vsn = (msn + ma) * Vа1.

Vа1 = mсн * Vсн / (mсн + ma).

Vа1 = 10 kg * 2780 km / h / (10 kg + 2000 kg) = 13.8 km / h.

The speed component directed along the road will decrease.

mа * Vа = (mа + mсн) * Vа2, where Vа2 is the vehicle speed directed along the highway after being hit by a shell.

Vа2 = ma * Vа / (ma + mсн).

Vа2 = 2000 kg * 50 km / h / (2000 kg + 10 kg) = 49.8 km / h.

The resulting movement speed will be the hypotenuse of a right-angled triangle with legs Vа1 = 13.8 km / h and Vа2 = 49.8 km / h.

tgφ = Vа1 / Vа2.

∠φ = arctgVа1 / Vа2.

∠φ = arctg (13.8 km / h / 49.8 km / h) = 15 °.

Answer: the car will move at an angle ∠φ = 15 ° to the highway