2 rockets are launched at a fireworks performance.Rocket A is launched with an initial velocity Vo and rocket

Question

B is

launched 4s later with the same initial velocity. the two

rockets are timed to explode simultaneously at a height of

80m, as A is a falling and B is rising.Assuming a constant

acceleration g=9.81m/s^2,determine(a)the initial velocity

Vo(b) the velocity of B relative to A at the time of the

explosion.

Answer 1

At first sight there are too many unknowns .. the initial rocket mass, fuel mass, rate of fuel usage and specific impulse of rocket motors are all unknowns needed to calculate the acceleration & hence flight profiles of each rocket.

We do know that A is falling .. so by the time 80m is reached A must have exhausted it's fuel and it's velocity must have been reduced by gravity to zero - however this is insufficient for us to calculate how long it takes to reach 80m - a very powerful motor would have pushed A well above 80m and would thus have resulted it a very long time for it to fall back down ...

We know that rocket B will have reached the same height by the time A falls back to 80m, despite having 4 seconds less time to do so, so this must place some constraints of A's flight profile...

This suggests there must be a range of answers for B initial velocity .. plainly if it is equipped with an extremely powerful motor, then it's initial velocity could be zero (or even negative) and it will still reach 80m in time) - whilst a less powerful motor but a higher initial velocity will still allow it to reach 80m at the right time ..

However we keep coming back to 'time ' .. if B has zero initial velocity and a motor that only just exceeds gravity (but virtually unlimited fuel), it can take a very long time to reach 80m .. and this allows A to have a very powerful motor (but limited fuel) and thus overshoot 80m and take a very long time to fall back ....

So thus also we end up with a range of relative velocities .. A might have only just reached 80m before falling back to meet B rising at high speed .. or  A may be falling back at high speed to meet B rising a low speed..

On the other hand, it could be that the moron who set the homework question is incapable of understanding the difference between a 'rocket' and a 'bomb' :-)