# Rocket car problem, find final velocity.

• stangeroo
In summary, the conversation discusses a physics problem involving a rocket attached to a car and a parachute. The car passes the judges' box 990 meters from the starting line 12 seconds after the rocket is fired. The conversation discusses using equations to solve for the car's speed at this point and provides guidance on how to approach the problem. There is a mistake in one of the equations used, but it is corrected.
stangeroo
We have to solve this problem, but also do a write-up on it similar to how the textbook gives example problems. Here is the problem:

Your school science club has devised a special event for homecoming. You've attached a rocket to the rear of a small car. The rocket provides a constant acceleratoin for 9 seconds. As the rocket shuts off, a parachute opens which slows the car at a rate of 5m?s^2. The car passes the judges' box 990 meters from the starting line 12 seconds after you fire the rocket. What is the car's speed as it passes the judges?

So after drawing a pictorial diagram I came up with the following info.

$$V_0$$=0
$$X_0$$=0
$$T_0$$=0

A=?

$$V_1$$=?
$$X_1$$=?
$$T_1$$=9

A=-5

$$V_2$$=?(the main thing youre trying to find)
$$X_2$$=990
$$T_2$$=12

I figure you need to find all the info out about the middle point, when the rocket shuts off and the parachute opens. And it seems like you need to work from the end backword, but I don't know how. Any help would be greatly appreciated

Last edited:
for the first leg (when rockets are fired up)
let the distance (unknown) be d1
t = 9 s
v1 = 0
v2 = ?
$a = a_{rocket}$

find this distance d1 in terms of v1, t and a(rocket)
now what is v2? v2 = v1 + a(rocket) t

now for the second leg of the journey
d = d2 (unknown)
t = 3s
v3 = v2
v4 doesn't matter
a = -0.5m/s^2
relate this distance d2 with the variable and constants that you have i.e. t, v3 = v2, and a.
d1 + d2 = 990
solve for a(rocket)
now solve for v2

You know your position equation, right?

$$x_f=x_i+v_i+\frac{1}{2}at^2$$

and your velocity equation:

$$v_f=v_i+at$$

You use both of those equations for both intervals.
Set up your equation for the first interval. Your final position over the first interval is the initial position for the second interval. Since you can't assign a number to the position, yet, you have to substitute the entire equation in as the initial position of your second interval. Once you do that, you'll only have one missing variable left: acceleration over the first interval.

Once you find the acceleration for the first interval, it's easy to find the velocity at the end of the first interval. Substitute that result for the initial velocity of your second interval and solve.

BobG said:
You know your position equation, right?

$$x_f=x_i+v_i+\frac{1}{2}at^2$$

and your velocity equation:

$$v_f=v_i+at$$

You use both of those equations for both intervals.
Set up your equation for the first interval. Your final position over the first interval is the initial position for the second interval. Since you can't assign a number to the position, yet, you have to substitute the entire equation in as the initial position of your second interval. Once you do that, you'll only have one missing variable left: acceleration over the first interval.

Once you find the acceleration for the first interval, it's easy to find the velocity at the end of the first interval. Substitute that result for the initial velocity of your second interval and solve.
ok, so the two equations for the first interval is

$$V_f1=9a$$and
$$X_f1=40.5a$$

Now I am not sure if i plugged them in right, but I got 20.45 as $$A_1$$

Put 990 as $$X_f$$, 40.5a as $$X_1$$, 9a for $$V_1$$, then -5 as $$a_2$$ and 3 for $$deltaT_2$$

Last edited:
ok, I got 2169.05 m/s for the velocity as it passes the judges, can someone else do the problem and tell me what you get.

That is incorrect.

"990 meters from the starting line 12 seconds after you fire the rocket", your answer is after the object slows down. If it ever traveled 2169.05 m/s ending time would be less than a second. I have not done the arithmetic, so the only suggestion I have is to check your units.

Edit: Take note of this, you should always check to see if your answer is logical.

ok, i think my error came from using the following equation:
$$x_f=x_i+v_i+\frac{1}{2}at^2$$

shouldnt there be $$t$$ after the $$v_i$$

stangeroo said:
ok, i think my error came from using the following equation:
$$x_f=x_i+v_i+\frac{1}{2}at^2$$

shouldnt there be $$t$$ after the $$v_i$$
Yes. Typo on my part Doesn't your book have these equations :craftily shifts blame: (What's up with the "craftily shifts blame" smiley? - it doesn't work. Oh, I see, wasn't crafty enough.)

BobG said:
Yes. Typo on my part Doesn't your book have these equations :craftily shifts blame: (What's up with the "craftily shifts blame" smiley? - it doesn't work. Oh, I see, wasn't crafty enough.)
lol, yea I have the equations, but out of laziness I just used the ones in this thread
, thanks for the help though

## 1. What is the Rocket Car Problem?

The Rocket Car Problem is a physics problem that involves calculating the final velocity of a car that is propelled by a rocket. It is commonly used as a thought experiment to demonstrate the principles of Newton's Laws of Motion.

## 2. What information is needed to solve the Rocket Car Problem?

To solve the Rocket Car Problem, you will need to know the mass of the car, the thrust of the rocket, the initial velocity of the car, and the amount of time the rocket is active. This information can be used to apply Newton's Second Law of Motion (F=ma) and the equation for calculating final velocity (v = u + at).

## 3. How do you calculate the final velocity of the rocket car?

To calculate the final velocity of the rocket car, you will need to use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (which is equal to the thrust divided by the mass of the car), and t is the time the rocket is active. Plug in the known values and solve for v.

## 4. What are the assumptions made in the Rocket Car Problem?

The Rocket Car Problem makes several assumptions, including that the rocket thrust is constant and that there is no air resistance. It also assumes that the rocket is the only force acting on the car and that the rocket engine is turned off after a certain amount of time.

## 5. How does the final velocity of the rocket car change with different variables?

The final velocity of the rocket car will change depending on the initial velocity, mass of the car, thrust of the rocket, and the time the rocket is active. For example, increasing the mass of the car will decrease the final velocity, while increasing the thrust of the rocket will increase the final velocity. The initial velocity and time the rocket is active will also have an impact on the final velocity.

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