An interstellar space probe is launched from the Earth. After a brief period of acceleration it moves with a constant velocity, with a magnitude of $70.0 \%$ of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 yr as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by Mission Control on the Earth? (b) How far is the probe from the Earth when its batteries fail as measured by Mission Control? (c) How far is the probe from the Earth when its batteries fail as measured by its built-in trip odometer? (d) For what total time interval after launch are data received from the probe by Mission Control? Note that radio waves travel at the speed of light and fill the space between the probe and the Earth at the time of battery failure.
here in five a Their darting I don t is in Quito, Commander. Tha tp there, there tp upon before time upon one minus bi bi si with But it was too 15 years. No poor time derided by one minus 0.70 Little squid, I'm so it is 21 1 Tzeitel here now for part B as measured by Mission Control, is opposed toe video dirty with oxygen to change and trying. Now here he is. You know 1700 c four to play time is 21 year begin Convert lightly light here into here and after. Then we will get 21 by the doe. The answer will be 14.7 light here Yuning toe idea No. In party, the astronauts see earth flying out through the back window at 0.700 C and B is equal to velocity into Delta Jota DP, which is proper time and swallow cities 0.700 c Multiply with delta T P, which is proper time is 15 years. No. After putting the values 0.700 multiply with proper time one year one leave here one leave here diverted by ear. Multiply with 15 point deedle years. We get the answer. One little want. Didn't want to fight? Yes, no. In part B, we have Mission Control Girls signals for 21.0 year while the battery is operating. And then 4 14.7 years after the battery stop. Spouting their transmitted 14.7 year light year of it, 14.7 light years away, 21.0 year plus 14.7 year it was Don't 35 17 years.