Arocket and a space station are both moving freely in deep interstellar space. the rocket is moving at speed 4/5 in the x direction as measured in the station’s (home) coordinate system. the rocket (other) coordinate system is in standard orientation relative to the station’s. an object is moving freely. observers on board the rocket measure the particle’s position to be x′ = 5s at time ′ = 4s and to be x′ = 8s at time ′ = 9s. show your work as you answer the following questions. a) what is the object’s velocity measured in the rocket coordinate system? b) what is the object’s velocity measured in the station’s coordinate system?

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1