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

Answer:

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

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

$0+0=6475.91\times v_1+234\times 170\cdot \cos (31.3)$

$v_1=-\frac{234\times 170\cdot \cos (31.3)}{6475.91}$

$v_1=-5.24 m/s$

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