# Rocket accelerating up an incline

• redworld33
In summary, a test rocket is launched from rest on an incline of length L and angle θ above the horizontal with constant acceleration a. When the rocket leaves the incline, its engines turn off and it is subject to only gravity. The position vector at the rocket's highest point can be found using the SUVAT equations and depends on the given variables. To find the position vector when the rocket is back at the top of the incline, we need to find the value of the final velocity at the end of the ramp, which will act as the initial velocity after it leaves the ramp. The maximum height can be found by knowing the height of the ramp, which can also be calculated using the given information.
redworld33
A test rocket is launched, starting on the ground, from rest, by
accelerating it along an incline with constant acceleration a. The incline has length
L, and it rises at θ degrees above the horizontal. At the instant the rocket leaves the
incline, its engines turn off and it is subject only to gravity, g≡+9.81m/s2. (Air resistance
can be ignored). Taking the usual x-y coordinate system, with an origin at the top edge
of the incline...

(a) What is the position vector when the rocket is at its highest point?
(b) What is the position vector when the rocket is on its way back down and once again at
the same height as the top edge of the incline?

depend on a, L, θ, g, and/or numerical factors.

I am so lost on this problemMy attempt:
Height of the incline = LSinθ
Angle: θ=arcsin(Height/L)

Horizontal velocity after rocket has finished accelerating up the incline = cosθ * sqrt(2aL)
Vertical velocity after the rocket has finished accelerating up the incline = sinθ * sqrt(2aL)

Last edited:
What equations do you know for constant acceleration motion? (Often called SUVAT equations.)

v^2 = v0^2 + 2a(x − x0)

x = x0 + v0t + ½at^2

v = v0 + at

Right. Each SUVAT equation involves four of five variables. To pick the one to use, you see which three variables you know and what variable you are trying to find. Then look for the equation using those four.
Now, thinking about the vertical direction, from leaving the launch ramp to maximum height, what three variables do you know and what variable are you trying to find?

we need vertical velocity to be 0 to find maximum height after leaving the ramp. this means we would have to find t when velocity equals 0, but after we find t what should I do? is there another SUVAT equation that yields y position at a specific time?

redworld33 said:
we need vertical velocity to be 0 to find maximum height after leaving the ramp. this means we would have to find t when velocity equals 0, but after we find t what should I do? is there another SUVAT equation that yields y position at a specific time?
Yes, and yes.
you will need to find t in order to get the x co-ordinate, and having found t you can use x = x0 + v0t + ½at^2 in the vertical direction. (If you only needed the max height, and didn't need to find t, you could have used v^2 = v0^2 + 2a(x − x0) to find max height.)

So I know this is an old thread, but possibly someone could help me because I have the same exact problem. I kind of understand the previous posts, yet, I am confused. In order to find the maximum height, which is not the height of the ramp, I would have to first find the value of the final velocity at the end of the ramp. This final velocity will then act as my initial velocity after it leaves the ramp and the velocity at tmax is 0. Although, to find my max height, wouldn't I also have to know the height of the ramp? I am confused, I didn't want to make a new thread, so hopefully this gets seen by someone!

zippeh said:
In order to find the maximum height, which is not the height of the ramp, I would have to first find the value of the final velocity at the end of the ramp. This final velocity will then act as my initial velocity after it leaves the ramp and the velocity at tmax is 0.
if you mean the vertical component of the velocity, yes.
Although, to find my max height, wouldn't I also have to know the height of the ramp?
Yes, but there's enough information given to find that.

## 1. How does the incline affect the rocket's acceleration?

The incline affects the rocket's acceleration by changing the direction of the force of gravity. When the rocket is on a flat surface, the force of gravity acts straight down and the rocket accelerates vertically. However, when the rocket is on an incline, the force of gravity is now acting at an angle, causing the rocket to accelerate both vertically and horizontally. This results in a slower vertical acceleration compared to when the rocket is on a flat surface.

## 2. Does the angle of the incline affect the rocket's acceleration?

Yes, the angle of the incline does affect the rocket's acceleration. The steeper the incline, the greater the horizontal component of the force of gravity and the slower the vertical acceleration. On the other hand, a shallower incline would result in a smaller horizontal component and a higher vertical acceleration.

## 3. How does the weight of the rocket affect its acceleration on an incline?

The weight of the rocket does not directly affect its acceleration on an incline. The acceleration is determined by the net force acting on the rocket, which is the difference between the force of gravity and the rocket's thrust. However, a heavier rocket would require a greater thrust to overcome the force of gravity and accelerate up the incline.

## 4. Is the rocket's acceleration constant on an incline?

No, the rocket's acceleration is not constant on an incline. As discussed earlier, the direction of the force of gravity changes with the incline, resulting in a changing acceleration. Additionally, the thrust of the rocket may also vary, causing fluctuations in the acceleration.

## 5. How does friction affect the rocket's acceleration on an incline?

Friction can have a significant impact on the rocket's acceleration on an incline. Friction acts in the opposite direction of the rocket's motion, slowing it down. This means that the net force acting on the rocket would be reduced, resulting in a lower acceleration. Therefore, minimizing friction is crucial in achieving a higher acceleration on an incline.

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