Question

A cannon on a railroad car is facing in a direction parallel to the tracks. It fires a 98.0-kg shell at a speed of 215 m/s (relative to the ground) at an angle of 60.0° above the horizontal. If the cannon plus car have a mass of 5.00 × 104 kg, what is the recoil speed of the car (relative to the ground) if it was at rest before the cannon was fired? Express your answer in m/s.

Answer 1

`v_c = 0.211 m/s`

Step-by-step explanation:

given,

mass of the shell = 98 kg

speed of the shell = 215 m/s

mass of the cannon + car = 5 × 10⁴ Kg

angle made with horizontal = 60°

velocity of recoil = ?

using momentum conservation because no other force component is acting

∑ P = 0

`m_s v_s+ m_(c)v_(c) = 0`

`v_s= v cos\theta`

`v_s = 215 cos60^0`

`v_s= 107.5`

now,

`v_c = (m_s v_s)/(m_c)`

`v_c = (98* 107.5)/(5 * 10^4)`

`v_c = 0.211 m/s`

velocity of the car is in negative direction of x.