Rocket Launch: Solving for Height and Time

[Dinovek]

Homework Statement

A rocket is launched off and accelerates vertically up at 10 m/s ². At 20 seconds, the motors are turned off, but the rocket keeps going up.

a) What height did it reach?
b) What was the time it needed to reach that height?

g: - 9.8 m/s²
a: 10 m/s²
final velocity: 0 m/s (Not sure).
t=20 s

Homework Equations

h= vo (t) + g(t)²/2
t=(vf-vo)/g
vo= vf-g(t)

The Attempt at a Solution

I needed to find initial velocity to find height so I did.

vo=vf-g(t)
vo= 0 m/s - (-9.8m/s²)(20)
vo= 196 m/s

Now I just substituted to find height.

h= vo(t) + (g (t)²)/2
h= 196 m/s (20s) + (-9.8 m/s² (20) ²)/2
h=3920 m + -3920 m/
h= 3920 m - 1960 m
h= 1960 m

I really have no clue how do to even start the problem because I'm not sure what is the time total. I was thinking that after it stops accelerating, every second it decreases 1 m/s on it's acceleration so that would 10 more seconds to the total timing.

Any help would be appreciated it. Thanks.

 

[VACA]

Why did you use g for acceleration during the first 20 seconds? The rocket is accelerating at +10m/s² during the first 10 seconds.

You would use g for acceleration after the 20 seconds, since that's when the motors are off.

 

[Dinovek]

Why did you use g for acceleration during the first 20 seconds? The rocket is accelerating at +10m/s² during the first 10 seconds.

You would use g for acceleration after the 20 seconds, since that's when the motors are off.

You're right, I didn't read carefully, thanks! I'm not sure how I'm going to calculate the total height. How do I know when it's going to reach final velocity of zero?

 

[VACA]

You're right, I didn't read carefully, thanks! I'm not sure how I'm going to calculate the total height. How do I know when it's going to reach final velocity of zero?

You first have to find the height it reaches in the first 20 seconds. V_f will not be zero after 20 seconds. After 20 seconds it is coasting (like a car when you take your foot off of the gas). It will take more time for it to reach 0 m/s (maximum height).

Try solving the coasting part on your own, and post back if you get stumped. Hint:

Spoiler

V_f when the motors are going will be V_o when the rocket is coasting.

 

[rwisz]

Hello! I can help you with this problem.

First, let's review the given information. The rocket is launched vertically and accelerates at a rate of 10 m/s2. This means that every second, its velocity increases by 10 m/s. At 20 seconds, the motors are turned off, but the rocket continues to move upward.

To solve for the height reached, we can use the equation h = vo(t) + (g(t)^2)/2, where h is the height, vo is the initial velocity, t is the time, and g is the acceleration due to gravity (which is -9.8 m/s2 in this case).

We already know that vo is 196 m/s (calculated correctly in your attempt), so we just need to find t. We can use the equation t = (vf - vo)/g, where vf is the final velocity (which is 0 m/s since the rocket stops accelerating at 20 seconds).

t = (vf - vo)/g
t = (0 m/s - 196 m/s)/ -9.8 m/s2
t = 196 m/s / 9.8 m/s2
t = 20 seconds

So, the rocket reaches its maximum height at 20 seconds. Now we can substitute this value into our first equation to solve for h.

h = vo(t) + (g(t)^2)/2
h = (196 m/s)(20 s) + (-9.8 m/s2)(20 s)^2/2
h = 3920 m + (-9.8 m/s2)(400 s^2)/2
h = 3920 m + (-9.8 m/s2)(200 s^2)
h = 3920 m - 1960 m
h = 1960 m

Therefore, the rocket reaches a height of 1960 meters at 20 seconds after launch. I hope this helps you understand the problem better. Keep up the good work with your calculations!