Question

A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched, of force constant 20000 N/m. The cannon fires a 237 kg projectile at a velocity of 170 m/s directed 31.3 â—¦ above the horizontal. 31.3 â—¦ If the mass of the cannon and its carriage is 6475.91 kg, find the recoil velocity of the cannon.

Answer 1

Step-by-step explanation:

Given

mass of cannon and cart is
`m_1=6475.91 kg`

Spring constant
`k=20000 N/m`

mass of Projectile
`m_2=234 kg`

Launch Velocity of cannon
`v_2=170 m/s`

Launch angle
`\theta =31.3^(\circ)`

As the External Force is zero therefore we can conserve momentum

Initially both Projectile and cannon is at rest

Conserving momentum in horizontal direction

`m_1u_1+m_2u_2=m_1v_1+m_2v_2\cos 31.3`

`0+0=6475.91* v_1+234* 170\cdot \cos (31.3)`

`v_1=-(234* 170\cdot \cos (31.3))/(6475.91)`

`v_1=-5.24 m/s`

i.e. cannon is moving in opposite direction of Projectile