(adsbygoogle = window.adsbygoogle || []).push({}); Rocket Problem, please help :)

1. The problem statement, all variables and given/known data

A rocket rises vertically, from rest, with an acceleration of 3.2 m/s^2 until it runs out of fuel at an altitude of 950 meters. After this point, it's acceleration is that of gravity, downward. a) What is the velocity of the rocket when it runs out of fuel? b) How long does it take to reach this point? c) What maximum altitude does the rocket reach? d) How much time (total) does it take to reach the maximum altitude?

2. Relevant equations

2a x Delta Y = Vf^2 - Vi^2

a = Delta V / t

Quadratic Formula

3. The attempt at a solution

First, I need to find the velocity of the rocket when it runs out of fuel.

I used 2a x Delta Y = Vf^2 - Vi^2

Plug in: 2 (3.2 m/s^2) (950 meters) = V^2 - 0

Answer: V^2 = 6080 m^2/s^2, thus V = 78 m/s

Second, I need to find how long it takes to reach this point.

I used a = Delta V / t and solve for t which makes: t = Delta V / a

Plug in: t = (78 m/s) / (3.2 m/s^2)

Answer: 24 seconds

Third, I need to find the maximum altitude the rocket reaches. Its already at 950 m once the fuel runs out.

I used 2a x Delta Y = Vf^2 - Vi^2, where Vi = 78 m/s, Vf^2 = 0 and a = g = -9.80 m/s^2

I solve for Delta Y, thus equation is Delta Y = Vf^2 - Vi^2 / 2a

Plug in: Delta Y = (0) - (78 m/s)^2 / 2 (-9.80), which = 6084 / 19.6 = 310 m

Answer: 310 m + 950 m = 1260 m or 1.26 km

Now here's where I get confused. I need to find the total time it takes to reach that maximum altitude of 1260 m. I already calculated that it took 24 seconds to reach 950 m, before decelerating and reaching zero velocity at 1260 m.

I used Delta Y = Vot + 0.5(-g)t^2

Plug in: 310 m = (78 m/s) t + (-4.90) t^2

I get: 4.9t^2 - 78t + 310 = 0

I use quadratic formula and I get 2 values for time, 7.7 and 8.2 seconds. Wtf?

Appreciate the help thank you

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# Rocket Problem, please help

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