An amateur scientist directs a radio signal pulse at Mars, which is 1.5 x 10m away at the time. Then, 800 seconds later, while peering through a telescope, she observes an explosion on Mars. Could the explosion somehow have been caused by her act of sending the radio pulse?

No.

Explanation:

A radio wave is an electromagnetic wave and all electromagnetic waves move at the speed of light, 3 * 10^8 m/s.

We can find the time it will take for the signal to get to Mars from Earth:

Time = distance/speed

Time = (1.5 * 10^11)/(3 * 10^8)

Time = 500 secs

Hence, it would be impossible for the explosion (which occurs 300 secs later) to have been caused by her radio signal pulse.

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

have a great day!