Solving a 1974 kg Weather Rocket Mystery

[BOTG]

Lost please help!

A 1974 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 20.27 s, then the motor stops. The rocket altitude 23.94 s after launch is 7242. You can ignore any effects of air resistance.

What was the rocket's acceleration during the first 20.27 s?
What is the rocket's speed as it passes through a cloud 7242 m above the ground?

 

[Dick]

The rocket is under a constant acceleration (call it 'a') during the first part of the trip (the first 20.27 secs), and under a constant acceleration of -g thereafter. You just have to splice these two solutions together. What equations do you know that govern motion under constant acceleration?

 

[nlightner]

I would approach this problem by first analyzing the given information and determining the variables needed to solve the mystery. From the information provided, we can determine that the rocket's mass is 1974 kg and that it experiences a constant acceleration for 20.27 seconds. We also know the rocket's altitude at 23.94 seconds after launch is 7242 m.

To solve for the rocket's acceleration during the first 20.27 seconds, we can use the equation: a = Δv/Δt, where a is acceleration, Δv is the change in velocity, and Δt is the change in time. Since we know the rocket's initial velocity is 0 m/s, we can calculate the change in velocity by dividing the final velocity (which we do not know) by the time of 20.27 seconds. Therefore, the acceleration during the first 20.27 seconds is a = v/20.27 s.

To solve for the rocket's speed as it passes through a cloud 7242 m above the ground, we can use the equation: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is acceleration, and s is the displacement. Since we know the rocket's initial velocity is 0 m/s, the equation simplifies to v^2 = 2as. We also know the acceleration from the previous calculation and the displacement of 7242 m. Therefore, we can solve for the final velocity, which is the rocket's speed as it passes through the cloud.

In conclusion, as a scientist, I would use mathematical equations and the given information to solve for the rocket's acceleration during the first 20.27 seconds and its speed as it passes through a cloud 7242 m above the ground. These calculations would help to solve the mystery and provide a better understanding of the rocket's behavior during its flight.