Mastering Physics 9.42 - Momentum of rocket/debris

AI Thread Summary
A 1500 kg weather rocket accelerates upward at 10 m/s² and explodes 2 seconds after liftoff, breaking into two fragments of differing masses. The lighter fragment ascends to a maximum height of 530 m, prompting the question of the heavier fragment's speed post-explosion. Calculations indicate an initial velocity of 20 m/s and a momentum of 30,000 kg*m/s, leading to the equation p_f = 1000*v_f_1 + 500*v_f_2. Despite multiple attempts yielding answers between 20.8 and 21.0 m/s, the solution remains incorrect, possibly due to significant figure discrepancies. The discussion emphasizes the importance of precision in calculations and the nuances of the Mastering Physics platform's grading criteria.
kramerbaggins
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Homework Statement



A 1500 kg weather rocket accelerates upward at 10m/s^2. It explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m.

That is the problem.

What was the speed of the heavier fragment just after the explosion?

That is the question.

I solved and got 20.96 m/s. It gives me this error:

You are close. You may have made a rounding error or used the wrong number of significant figures.

Homework Equations



Using the 10m/s^2 * 2s, i got the v_i to be 20 m/s, p_i then is 30000 kg*m/s.

p_f is 1000*v_f_1 + 500*v_f_2

Used v_f^2 = v_i^2 + 2*a*s on the smaller mass fragment. Used v_f = 0, a = -9.8, s given in problem. Solved for v_i. This v_i is the inital velocity of the fragment, aka its velocity at the end of the explosion.

Set 30000 = 1000*v_f_1 + 500*v_f_2, using v_f_2 from dynamics equation work above. solved for v_f_1.

The Attempt at a Solution

 
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At a glance, your work seems to be correct. One possibility, as it says, is that you are using the wrong number of significant figures. You have 4, how many appear in the numbers in the problem?
 
Well Mastering Physics really doesn't care how many are in your answer as long as it is within like .05 or so. I ahve tried two different answer very close to 21, but still nothing
 
Ive tried from 20.8-21.0, but still wrong. It is from 20-22 I am assuming, but idk
 
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