rocket moves from the rest by acceleration upward at 30 for 30 s what is the rocket max altitude?

Question

after 30 s this rocket roun the fuel how long is the rocket in the air and what is the velocity of the rocket at the time 100 s from the moment when the engine stoped

after 30 s this rocket roun the fuel how long is the rocket in the air and what is the velocity of the rocket at the time 100 s from the moment when the engine stoped

after 30 s this rocket roun the fuel how long is the rocket in the air and what is the velocity of the rocket at the time 100 s from the moment when the engine stoped

Answer 1

Ok, what I understood, is that the acceleration of the rocket is 30 m/s^2, and after 30 seconds, the rocket went out of fuel, so then :

Vo = 0 m/s >>> initial speed

acceleration = 30 m/s^2 - gravity

let's consider g = 10 m/s^2

We need to find out first, the altitude and the final velocity after 30 seconds :

H = 1/2*20*900 = 9000 meters

Vf^2 = 2*20*9000

Vf = 600 m/s

So the rocket is 9000 meters over the ground, and has a velocity of 600 m/s, now, let's find the maximum altitude with :

Second part

Now, I will consider an initial speed of : 600 m/s

the desacceleration of gravity : 10 m/s

Final velocity when the rocket reaches it's maximum altitude : 0 m/s

Here, I will find the time the rocket took to reache it's maximum altitude after the 30 seconds :

0 = 600 - g*t

t = 60 seconds

0 = 600^2 - 2*g*h

h = 18000 meters

the maximum altitude : h + H = 9000 + 18000 = 27000 meters

the rocket is now 27000 meters over the ground, and the total time was : 90 seconds.

Third part :

You asked the velocity after 100 seconds, after the first 30 seconds, right ?, so, let's just consider 60 seconds has passed :

Vo = 0 m/s

t = 40 s

Vf = 10*40 = 400 m/s >>> velocity, 100 seconds, after the rocket went out of fuel