Designing a toy rocket to be launched by a spring

[ProBasket]

You're designing a toy rocket to be launched by a spring. The launching apparatus has room for a spring that can be compressed 14 cm, and the rocket's mass is 65 g. If the rocket is to reach 35 m altitude, what should be the spring constant?

U_o = 1/2*kx^2
K_o = 0
well work is being stored so K = 0 and U has the spring energy right?

U_f = mgh
K_f = 0

U_f = mgh because of the gravitational potention energy right? and K_f = 0 because it's at rest right when it reaches 35m? I'm not sure if K_f = 0 or not because i don't really know if the rocket is at it's max height when it reaches 35m.

well, setting them equal to each other...
1/2*kx^2 = mgh and solving for k, i get 3.1 but the book gets 2.3 kN/M. what am i doing wrong?

 

[xanthym]

You're designing a toy rocket to be launched by a spring. The launching apparatus has room for a spring that can be compressed 14 cm, and the rocket's mass is 65 g. If the rocket is to reach 35 m altitude, what should be the spring constant?

U_o = 1/2*kx^2
K_o = 0
well work is being stored so K = 0 and U has the spring energy right?

U_f = mgh
K_f = 0

U_f = mgh because of the gravitational potention energy right? and K_f = 0 because it's at rest right when it reaches 35m? I'm not sure if K_f = 0 or not because i don't really know if the rocket is at it's max height when it reaches 35m.

well, setting them equal to each other...
1/2*kx^2 = mgh and solving for k, i get 3.1 but the book gets 2.3 kN/M. what am i doing wrong?

Your work is correct except for UNITS. Recalculate ALL quantities in MKS (meter, kg, sec) units, and you'll obtain the book answer.


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[thepatientmental]

Your calculations and approach are correct. The book may have rounded the answer to 2.3 kN/M for simplicity. It is also possible that there was a typo in the book. It is always good to double check your work and use multiple sources for confirmation. Good job on solving the problem!