Question

A cannon on a railroad car is facing in a direction parallel to the tracks. It fires a 97.00 kg shell at a speed of 105 m/s (relative to the ground) at an angle of 60.0° above the horizontal. If the cannon plus car have a mass of 4.9 × 104 kg, what is the recoil speed of the car if it was at rest before the cannon was fired?

Answer 1

Answer:

recoil velocity of canon is 0.1039 m/s

Explanation:

given,

mass of shell = 97 kg

speed at which the shell is fired = 105 m/s

angle at which the shell is fired (θ) = 60°

mass of cannon plus car = 4.9 × 10⁴ kg

by conservation of momentum

    ∑ P = 0

$P_{initial} +P_{final} = 0$

$m_{cannon}v_{cannon} +m_{shell}v_{shell} = 0$

$v_{cannon}=\dfrac{m_{shell}v_{shell} cos\theta}{m_{cannon}}$

$v_{cannon}=\dfrac{97\times 105\times cos 60^0}{4.9\times 10^4}$

$v_{cannon} = 0.1039\ m/s$

recoil velocity of canon is 0.1039 m/s