Question

A 900-kg rocket is released from a space station. As it burns the fuel, the rocket’s mass
decreases and its velocity increases. Let v(m) be the velocity in m/s as a function of mass. Find the
velocity when m=729 kg if 𝑚′(𝑣) = −50𝑚^(−0.5). Assume that v(900)=0.

Answer 1

dm/dv = -50/√m
√m dm = -50 dv
2/3 m^(3/2) = -50v + C
since v=0 when m=900,
2/3 * 27000 = C
so, now you have
2/3 m^(3/2) = -50v + 18000
Now find v when m = 729
2/3 * 19683 = 18000 - 50v
v = _____