Rocket problem -- separated fuel tank in free fall

[Adeopapposaurus]

Homework Statement

The fuel tank detaches from the rocket rising vertically upwards when it has velocity v_1. Calculate the final time t and the speed with which the tank falls to the ground. Given is the gravitational acceleration g, the air resistance should be omitted

Relevant Equations

v = v₀ + gt
s = v₀t + (1/2)gt²

I know that this should be a very simple problem, but I don't understand how to solve it without knowing the height at which the tank is separated from the rocket. I will be very grateful for any hint.

 

[Ibix]

Have you reproduced the entire question exactly as it's written? It reads like part two of a question and there may be more relevant information in the earlier parts.

If there is not more information then I don't see how the problem can be solved.

 

[haruspex]

Homework Statement:: The fuel tank detaches from the rocket rising vertically upwards when it has velocity v_1. Calculate the final time t and the speed with which the tank falls to the ground. Given is the gravitational acceleration g, the air resistance should be omitted
Relevant Equations:: v = v₀ + gt
s = v₀t + (1/2)gt²

I don't understand how to solve it without knowing the height at which the tank is separated from the rocket.

Clearly you need that or some other additional information. You can prove that by supposing it happens at height h, getting a solution in which h appears, and checking that your solution does not violate any of the given info.