I got following:
3km/s*100days*24hours/day*3600seconds/hour = 25920000km
Than I let my scientific calculator solve the equation:
25920000km+3km/s*Xs = 300000km/s*Xs
wich found out hat X (the seconds the signal needs) is:
X = 86,40086401s
and the signal gets the probe at 25920259,2km, but I think it's periodic and my calculator shortened it, so I think X = 86,4008640086400864008640086400..... (86400 again and again) s
and the signal gets the probe at 25920259,2025920259202592025920.... km
I would have answered:
flying away from earth at a velocity of 3km/s is too slow - it isn't even in an Orbit, so it would crash down within the 100 days. So the time is depending from the radio stations postition and the probes crashdown-position, but not longer than: 12756km(earth diameter)/300000km/s = 0,04252s
:lol:
---------- Post added at 17:25 ---------- Previous post was at 17:19 ----------
About the Algebra II textbook I mentioned earlier, I actually found an example problem involving spaceflight (I haven't gotten to natural logarithms yet):
"A spacecraft can attain a stable orbit 300 km above Earth if it reaches a velocity of 7.7 km/s. The formula for a rocket's maximum velocity v in kilometers per second is v = -0.0098t + c ln R. The booster rocket fires for t seconds and the velocity of the exhaust is c km/s. The ratio of the mass of the rocket filled with fuel to its mass without fuel is R."
The example then gives some numbers for the variables and shows how to solve it (using a calculator). A caption beside the example problem states that escape velocity from Earth is 11.2 km/s. What do you think about this formula? Does it only apply to single stage to orbit rockets?
The formula is only right for rockets wich onlylaunch straight up from earth.
I would use the formula: deltaV=c*lnR for the exhaust speed I set in the efficiency in N*s/kg instead, because than it's also correct for air-breathing engines, and other special cases.
For multistage-rockets I calculate the deltaV for each stage seperately.
I fill in gravity ad air-drag when I find out how much deltaV the rocket needs at all.