Sample Problem

Sample Problem

Shows a space hauler and cargo module. of total mass M traveling along an x axis in deep space. They have an initial velocity VI of magnitude 2100 km/h relative to the Sun. With a small explosion. the hauler ejects the cargo module. of mass . The hauler then travels 500 km/h faster than the module along the x axis; that is the relative speed between the hauler and the module is 500 km/h. What then is the velocity  of the hauler relative to the Sun.

SOLUTION: The Key Idea here is that. because the hauler-module system is closed and isolated. its total linear momentum is conserved; that is.

where the subscripts I and f refer to values before and after the ejection. respectively. Because the motion is along a single axis. we. can write momenta and velocities in terms of their x components. Before the ejection. we have

(a) A space hauler. with a cargo module. moving at initial velocity VI' (b) The hauler has ejected the cargo module. Now the module has velocity VMS and the hauler has velocity vH
(a) A space hauler. with a cargo
module. moving at initial velocity VI’ (b) The hauler has ejected
the cargo module. Now the module has velocity VMS and the
hauler has velocity vH

Substituting this expression for MS into . and then substituting. we find

CHECKPOINT 5: The table gives velocities of the hauler and module (after ejection and relative to the Sun). and the relative speed between the hauler and the module for three situations. What are the missing values?

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