How Does a Rocket Behave After Engine Shutdown?

[hantheman]

A rocket is fired vertically upwards with an initial velocity of 80 m/s with an acceleration of 4 m/ss until it reaches an altitude of 1000m. At that point it goes into free fall (a= -9.8)

What time interval is the rocket in the air?
What is its maximum altitude?
What is its velocity right before it hits the ground?


Does this mean that the rocket continues to go upwards after the engine fails?

I got the time until that point to be 10 seconds and the final velocity a that point (1000m) to be 120 m/s. Afterward, all I can come up with is a initial velocity of 120 m/s and gravitational acceleration. I can't find t without another variable.

Thanks in advance

 

[Kalvarin]

You need to calculate the distance the rocket travels after the engine fails before it comes to a complete stop.

 

[tomcue]

for your response!

I can confirm that the rocket will indeed continue to go upwards after the engine fails. This is due to the law of inertia, which states that an object in motion will continue to move in the same direction and at the same speed unless acted upon by an external force.

To answer your questions, we can use the equation for displacement (s=ut+1/2at^2) to find the time interval. Plugging in the given values, we get:

1000m = 80m/s * t + 1/2 * 4m/s^2 * t^2

Solving for t, we get t = 10 seconds. This means that the rocket is in the air for 10 seconds.

To find the maximum altitude, we can use the equation for displacement again. This time, we plug in the initial velocity (80m/s), the time (10 seconds), and the acceleration (-9.8m/s^2). This gives us:

s = 80m/s * 10s + 1/2 * -9.8m/s^2 * (10s)^2 = 400m

Therefore, the maximum altitude reached by the rocket is 400 meters.

To find the velocity right before it hits the ground, we can use the equation for velocity (v=u+at). Plugging in the values, we get:

v = 80m/s + (-9.8m/s^2) * 10s = -2m/s

This means that the velocity right before the rocket hits the ground is -2m/s, indicating that it is moving downwards.

In conclusion, the rocket will continue to go upwards after the engine fails, reaching a maximum altitude of 400 meters before falling back to the ground with a velocity of -2m/s. I hope this explanation helps to clarify any confusion.