# Projectile Motion Rocket Problem

• TheRedDevil18
In summary, the rocket reached its maximum height of 308.18 m after lift-off, and remained in the air for 17.04s.
TheRedDevil18

## Homework Statement

A model rocket is launched vertically upwards with an initial speed of 50m/s. It accelerates with a constant upward acceleartion of 2m/s until its engine stop at an altitude of 150m.

2.4.1) What is the maximum height reached by the rocket?
2.4.2) How long after lift-off does the rocket reach maximum height?
2.4.3) How long is the rocket in the air?

## Homework Equations

equations of motion

## The Attempt at a Solution

2.4.1) To get the max height I first found the final velocity of the rocket before the engine was switched off. I got this to be 55.68m/s. I then used this to find the height reached after the engine was switched off by making it the initial velocity and using the acceleration of 9.8m/s. I got this to be 158.18m. So the max height is 308.18m.

2.4.2) By breaking the problem into two parts(one 150m and the other 158.18m)I got the times to be 2.84s and 5.68s. Adding them up gives me 8.52s to reach its max height.

2.4.3) Multiplied the time by two(going up and coming down) to get 17.04s.

Please could someone check my work, any help would be greatly appreciated

The methods in part 1 and part 2 are correct (not sure about the numbers). The method for part 3 is wrong, the acceleration profiles are different on the way up and down.

Numbers in parts 1 and 2 are correct. Ditto the comment by voko about part 3.

Could you refer to the question number?, on the way up I used 2m/s(given), and when the engines where switched off I used 9.8m/s.

TheRedDevil18 said:
Could you refer to the question number?, on the way up I used 2m/s(given), and when the engines where switched off I used 9.8m/s.
Everyone agrees with what you did for 2.4.1 and 2.4.2. But you cannot simply multiply the ascent time by two to get the total time in the air. It's not symmetric. Compute descent time separately.

Thats what I did in 2.4.2, I broke the problem up and got the times to be 2.48s and 5.48s. Adding them up gave me 8.52s to reach max height. The time going up must equal the time coming down, am I right?, and so that's why I multiplied the time by 2.

TheRedDevil18 said:
The time going up must equal the time coming down, am I right?

Why is that so?

TheRedDevil18 said:
Thats what I did in 2.4.2, I broke the problem up and got the times to be 2.48s and 5.48s. Adding them up gave me 8.52s to reach max height. The time going up must equal the time coming down, am I right?, and so that's why I multiplied the time by 2.
Only if the projectile is symmetric eg. parabola.

Is the final answer 14.77s?, because I think I hit a miss with the acceleration for the second part where I used 2m/s instead of 9.8m/s coming down.

How long does it take for the body to come from the max height down to the ground? What equation gives this time?

voko said:
How long does it take for the body to come from the max height down to the ground? What equation gives this time?

It takes 6.26s to hit the ground starting from max height? I used the equation vf = vi+a*t.

Explain how you used the equation. What are vi and vf in your case?

When the planes engines where switched off:
0 = 55.68+(9.8)t
t = 5.68s

For the remaining 150m:
55.68 = 50+9.8t
5.68 = 9.8t
t = 0.58

Adding it up gives you 6.26s.

Okay, is the answer 7.93s to fall from max height?, I just worked it out now.

7.93 s is correct, assuming the max height is indeed 308.18 m.

So the total time in the air is (8.52s to go up + 7.93s to come down) = 16.45s

## 1. What is projectile motion and how does it apply to a rocket problem?

Projectile motion is the movement of an object through the air or space under the influence of gravity. In a rocket problem, projectile motion is used to calculate the trajectory, velocity, and acceleration of a rocket as it moves through the air.

## 2. How is the initial velocity of a rocket determined in a projectile motion rocket problem?

The initial velocity of a rocket is determined by the force of the rocket's engines as it launches. This force, along with the mass of the rocket, can be used to calculate the initial velocity using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

## 3. What factors affect the trajectory of a rocket in a projectile motion problem?

The trajectory of a rocket is affected by the initial velocity, the angle of launch, and the force of gravity. Other factors such as air resistance and wind can also play a role, but are typically negligible in most projectile motion rocket problems.

## 4. How is the maximum height and range of a rocket calculated in a projectile motion problem?

The maximum height and range of a rocket can be calculated using the equations h = u2sin2(θ)/2g and R = u2sin(2θ)/g, where h is the maximum height, R is the range, u is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

## 5. Can projectile motion be used to accurately predict the flight of a rocket?

Yes, projectile motion can be used to accurately predict the flight of a rocket as long as the initial conditions and factors affecting the trajectory are known. However, external factors such as air resistance and wind may cause slight variations in the actual flight of the rocket.

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