(a) 8927 mi/h
In order to calculate the average speed, we need to convert the time (t=5.0 y) into hours first. In 1 year, we have 365 days, each day consisting of 24 hours, so the time taken is:
[tex]t=(5.0 y)(365 d/y)(24 h/d)=43,800 h[/tex]
The distance covered by the spacecraft is
[tex]d=391 mil. mi = 391\cdot 10^6 mi[/tex]
Therefore, the average speed is just the ratio between the distance covered and the time taken:
[tex]v=\frac{d}{t}=\frac{391\cdot 10^6 mi}{43,800 h}=8,927 mi/h[/tex]
(b) 35 minutes (2097 seconds)
The transmitted signals (which is a radio wave, which is an electromagnetic wave) travels back to the Earth at the speed of light:
[tex]c=3.0\cdot 10^8 m/s[/tex]
Since 1 miles = 1609 metres, the distance covered by the signal is
[tex]d=391\cdot 10^6 mi \cdot (1609 m/mi)=6.29\cdot 10^{11} m[/tex]
So, the time taken by the signal will be
[tex]t=\frac{d}{v}=\frac{6.29\cdot 10^{11} m}{3.0\cdot 10^8 m/s}=2097 s[/tex]
And since 1 minute = 60 sec, the time taken is
[tex]t=2097 s \cdot \frac{1}{60 s/min}\sim 35 min[/tex]
