Q. A 10.6 kg weather rocket generates a thrust of 226.0 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 402.0 N/m, is anchored to the ground. Initially, before the engne is ignited, the rocket sits at rest on top of the spring.

Question

A: After the engine is ignited, what is the rocket's speed when the spring has stretched 19.4 cm past its natural length?

B: What would be the rocket's speed after travelling the distance if it weren't tied down to the spring?

Attemp:
i used 1/2kx^2+Fthrust(d) = 1/skx^2 + mg(d) + 1/2mv^2 to solve (A) but i'm getting the wrong answer and i also used 3 other equations to solve this but they all wrong.
i have no idea how to start part (B)

Answer 1

Ok, net force upward pulling on the spring is thrust-mg

That net force * distance= 1/2 k distance^2 + 1/2 m v^2

Assume mass of rocket stays same, in reality, it does not as fuel is burned. Make certain distance is in meters, v in m/s

If not tied to spring..

Vf^2=2ad where a= net force/mass

Answer 2

Thank You!!!