Can anyone answer the following problem? It has me stumped. A water jet strikes

Question

Can anyone answer the following problem? It has me stumped.

A water jet strikes a cart as shown. After striking the cart, the water is deflected vertically with respect to the cart. The cart is initially at rest and is accelerated by the water jet. The mass in the water jet is much less than that of the cart. There is no resistance on the cart. The mass flow rate from the jet is 4S kg/s. The mass of the cart is 100 kg. Find the time required for the cart to achieve a speed one-half of the jet speed.<?xml:namespace prefix = o />

Explanation / Answer

Mc(mass of cart) * a(cart acceleration) = -m(dot) * [V (sub 2) - V (sub 1)] and account for the fact that Vj (velocity of the jet) is relative to Vc (velocity of the cart). Initial velocity of the cart is zero (Vc1 = 0)

        = -m(dot) * [(Vj-Vc)2 - (Vj-Vc)1]
        = -m(dot) * [(Vj-0.5Vj)2 - (Vj-0)1] :combine like terms.

        = -m(dot) * (Vj - 0.5Vj - Vj)

        = -m(dot) * -(0.5Vj)

M*a = m(dot) * 0.5Vj

Now use Vc = 0.5*Vj= V(sub zero)(cart initial velocity) + a(cart acceleration) * t (time) to calculate speed.

solving for t = (2*Mc*Vj) / (2*m(dot)*Vj) = Mc / m(dot) = 100/45 = 2.22 seconds.

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