A space utility vehicle has lost all power and is at rest in outer space. To get

Question

A space utility vehicle has lost all power and is at rest in outer space. To get it moving, two pieces of the failed engine are ejected simultaneously. One piece has mass M=15 kg and is e ected with speed V-56 m/s in the i direction. The other piece has mass m=10 kg and is ejected with speed v=16 m s in the j direction. Without those pieces, the vehicle has mass Msu,-59 kg. Calculate the new velocity of the vehicle. PAPER SOLUTION INTERPRET DEVELOP In your answers below, type Msuv to represent M Derive an algebraic expression for the new velocity. Derive an algebraic expression for the new speed. EVALUATE Calculate a numerical value for the new velocity. Vv-14.23 m/si-2.7 m/s j Calculate a numerical value for the new speed. V14.48 m/s Calculate a numerical value for the direction of motion (counterclockwise from i, as usual). degrees

Explanation / Answer

Given

M = 15 kg , V = 56 m/s along x direction

m = 10 kg , v = 16 m/s along y direction

M suv = 59 kg

momentum along x direction is Px = M*Vx = mSuv*vsuv_x ==> V_suv_x = M*V /MSuv i = 15*56/(59) m/s = 14.23 m/s

along y direcrion is Py = M*Vy = mSuv*vsuv_y ==> V_suv_y = m*v /MSuv j = 10*16/(59) m/s = 2.711 m/s

V = M*V /MSuv i +m*v /MSuv j

V suv = 14.223 m/s i + 2.711 m/s j

the magnitude is V = sqrt(Vx^+Vy^2) = sqrt(14.223^2+2.711^2) m/s= 14.48 m/s

theta = arc tan (Vy/vx) = arc tan (2.711/14.233) = 10.78 degrees

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