Homework Help: Kinematics problem

1. Jan 13, 2008

emilinus

I just need help getting started with this question.

A 1350.0 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 10.2 s, then the motor stops. The rocket altitude 26.9 s after launch is 2210.0 m. You can ignore any effects of air resistance. What was the rocket's acceleration during the first 10.2 s?

total distance is 2210.0 m
acceleration during 10.2 s and 26.9 s is -9.81 m/s^2
the acceleration during t=0 s and t=10.2 s is cst.

2. Jan 13, 2008

olgranpappy

you have a kinematic equation which relates position velocity and acceleration, something like:
$$x = \frac{1}{2}at^2+v_0 t+x_0\;.$$
a is accleration, v_0 is initial velocity, x_0 is initial position, x is position at time t. First of all, what are x_0, and v_0?

3. Jan 13, 2008

emilinus

but say x_0 and v_0 are both 0...you're still left with two variables...

ie x = 52.2a well that's for the first section t=0 to t=10.2

4. Jan 14, 2008

olgranpappy

you are given both 'x' and 't' in the third sentence of the question. plug them in and solve for 'a'.

5. Jan 14, 2008

emilinus

that would give the acceleration during t=10.2 s and t=26.9 s...which is different from the acceleration during t=0 s to t=10.2 s

6. Jan 14, 2008

olgranpappy

oh... right, I see.

Well, you can work in two steps. For the first 10.2 seconds you already know that x(t) = 1/2 at^2

so you can find the position at t=10.2 (in terms of a) and the velocity at t=10.2 (in terms of a). Call these things x_1 and v_1, respectively.

Next, you can use the "free fall" kinematic equations (i.e., the usual equation with a=-g=-9.8m/s^2) to do the rest of the problem; just use v_1 and x_1 where you would normally have used v_0 and x_0. And use (t-10.2) where you would normally have used t.

P.S. Draw a picture of what's going on, that should help a bit and help you organize what is happening to the rocket.