Calculating Final Velocity of Two Objects

[woolford85]

A space vehicle traveling at a velocity of 100m/s separates by a controlled explosion into two sections of mass 850kg and 250kg. The two parts carry on in the same direction with the heavier rear section moving 120m/s slower than the lighter front section. Determine the final velocity of each section.



I have tried to look at a way of solving this using SUVAT but there are too many unknowns to use these equations. This question is part of an assignment I have to do, I need to know if it is even possible to do these calculations with the information that I have been given. If anyone could help me that would be great, thanks.

Michael

 

[Varadha]

Use conservation of momentum

I guess we can use the law of perfect collision in 1-dimension,

Total mass initially be, M = 850 + 250 = 1100 kg
Total initial momentum will be, p = 1100*100 = 110000 kg.m/s

After the splitting, we have two masses. The velocities of heavier mass be v¹and that of the lighter mass be v².

Total momentum after splitting will be, 850v¹ + 250v²

It is also given that heavier section moves at a speed 120 m/s slower than the lighter section. Therefore, v¹ = v² - 120

By the law of conservation of momentum, we have initial momentum = final momentum

110000 = 850v¹ + 250v²

Substituting v¹ = v² - 120,

110000 = 850(v² - 120) + 250v²
110000 = 1100v² - 120*850
8000 = 1100v²
therefore, v² = 7.273 m/s and
v¹ = 127.273 m/s

Hope I am correct

 

[Varadha]

Sorry.. I have used superscripts 1 and 2 instead of subscript. Pardon