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**1. Homework Statement**

A 11.7 kg weather rocket generates a thrust of 240 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 560 N/m, is anchored to the ground.

(a) Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?

20.5cm (.205m)

(b) After the engine is ignited, what is the rocket's speed when the spring has stretched 33.0 cm?

2.87m/s

(c) For comparison, what would be the rocket's speed after traveling this distance if it weren't attached to the spring?

This is the question I have a problem with.

**2. Homework Equations**

Ug = mgh

Us = 1/2 k (delta_x)^2

KE = 1/2mv^2

W_thrust = F_thrust*distance

**3. The Attempt at a Solution**

Ok, so for Part (b) I used the following equation to find the velocity:

W_thrust + U_s(using x_1) = U_s(using x_2) + U_g + KE

I was able to solve for the v in KE correctly using this equation. So in order to find the velocity of the rocket when the spring is taken out, I take the U_s out of the equation:

W_thrust = U_g + KE Where the distance here will be x_1 + x_2. (x_compressed + x_stretched = x_total)

I've done this problem a number of ways.. work, energy, kinematics.. and i keep arriving at the (incorrect) answer v = 3.38m/s. Can anyone help me spot my error? Thanks in advance.

-Sam

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**

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