The cart has a mass of 3 kg and rolls freely from A down the slope. When it reaches the bottom, a spring loaded gun fires a 0.5-kg ball out the back with a horizontal velocity of m/s, measured relative to the cart. Determine the final velocity of the cart.

V_c=5.037 m/s

Explanation:

SOLUTION:

applying the conversation of energy, taking the datum at B

V_b=(m_c+m_b)gh_a=(3+0.5)*9.81*0=0 J

V_b=4.95 m/s

applying the conversation of linear momentum,

(m_c+m_b)V_b=m_c*V_c+m_b*V_b

V_b=6*V_c-34.66            (1)

utilising the relative velocity relation,

V_b/c=V_b-V_c

V_b=0.6-V_c                      (2)

from (1) (2)

6*V_c-34.66=0.6-V_c

7*V_c=35.26

the final velocity of the cart is

V_c=5.037 m/s

into (2)

V_b=0.6-V_c    

V_b=0.6-5.037

      = 4.437

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