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

Answer:

$v_c = 0.211 m/s$

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,

$v_c = \dfrac{m_s v_s}{m_c}$

$v_c = \dfrac{98\times 107.5}{5 \times 10^4}$

$v_c = 0.211 m/s$

velocity of the car is in negative direction of x.