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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.

Respuesta :

Answer:

Explanation:

Given

mass of cannon and cart is [tex]m_1=6475.91 kg[/tex]

Spring constant [tex]k=20000 N/m[/tex]

mass of Projectile [tex]m_2=234 kg[/tex]

Launch Velocity of cannon [tex]v_2=170 m/s[/tex]

Launch angle [tex]\theta =31.3^{\circ}[/tex]

As the External Force is zero therefore we can conserve momentum

Initially both Projectile and cannon is at rest

Conserving momentum in horizontal direction

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2\cos 31.3[/tex]

[tex]0+0=6475.91\times v_1+234\times 170\cdot \cos (31.3)[/tex]

[tex]v_1=-\frac{234\times 170\cdot \cos (31.3)}{6475.91}[/tex]

[tex]v_1=-5.24 m/s[/tex]

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

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