What is the Correct Speed of the Heavier Fragment in a Weather Rocket Explosion?

[physicsCU]

Not sure of the number, but it is about a weather rocket that explodes.

A 1500 kg weather rocket accelerates upward at 10\;{\rm m}/{\rm 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.

Help! What is the right answer?

 

[dextercioby]

How did u get that #...?How many sign.digits are u required to use...?

Daniel.

 

[physicsCU]

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.

EDIT: The system is evaluating my answer as 21.0, so i think my sig figs are right. Unless the server is broken, which could be the case.

 

[physicsCU]

Anyone have any ideas?