. A 50-kg model rocket lifts off by expelling fuel downward at a rateof k = 4.75 kg/s for 10 s. The fuel leaves the end of the rocket with anexhaust velocity of b = −100 m/s. Let m(t) be the mass of the rocketat time t. From the law of conservation of momentum, we find the following differential equation for the rocket’s velocity v(t) (in meters persecond):m(t)v(t) = −9.8m(t) + bdmdt(a) Show that m(t) = 50 − 4.75t kg.(b) Solve for v(t) and compute the rocket’s velocity at rocket burnout(after 10 s)

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