A spaceship is moving with constant speed $v_{0}$ in gravity free space along $+ Y$ axis suddenly shoots out one third of its part with speed $2 v_{0}$ along $+ X$ axis. The speed of the remaining part is $\frac{\sqrt{10 + x}}{2} v_{0}$ . Find $x$ .

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Solution

$B y c o n s e r v a t i o n o f m o m e n t u m, m_{1} {v_{1} + m}_{2} v_{2} = c o n s t a n t T h u s, M v_{0} \to j = \frac{M}{3} (2 v_{0}) \to i + \frac{2 M}{3} v_{x} \to i + \frac{2 M}{3} v_{y} \to j w h i c h g i v e s, v_{y} = 3 / 2 v_{0}, v_{x} = - v_{0} T h u s v = \sqrt{{v_{y}}^{2} + {v_{x}}^{2}} = \frac{\sqrt{13} v_{0}}{2} T h u s x = 13$

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A spaceship is moving with constant speed v0 in gravity free space along +Y axis suddenly shoots out one third of its part with speed 2v0 along +X axis. The speed of the remaining part is √10+x2v0. Find x.

Byconservationofmomentum,m1v1+m2v2=constantThus,Mv0→j=M3(2v0)→i+2M3vx→i+2M3vy→jwhichgives,vy=3/2v0,vx=−v0Thusv=√vy2+vx2=√13v02Thusx=13

A spaceship is moving with constant speed $v_{0}$ in gravity free space along $+ Y$ axis suddenly shoots out one third of its part with speed $2 v_{0}$ along $+ X$ axis. The speed of the remaining part is $\frac{\sqrt{10 + x}}{2} v_{0}$ . Find $x$ .