Answer
$P = 69~hp$
Work Step by Step
We can express the speed in units of $m/s$:
$v = (80~km/h)(\frac{1~h}{3600~s})(\frac{1000~m}{1~km}) = 22.22~m/s$
We can find the resistant force:
$F_r = 300+1.8~v^2$
$F_r = 300+(1.8)(22.22~m/s)^2$
$F_r = 1188.7~N$
We can find the required force:
$F-F_r = ma$
$F = ma+F_r$
$F = (\frac{12,000~N}{9.8~m/s^2})(0.92~m/s^2)+(1188.7~N)$
$F = 2315~N$
We can find the required power:
$P = F~v$
$P = (2315~N)(22.22~m/s)$
$P = 51,444~W$
$P = (51,444~W)(\frac{1~hp}{745.7~W})$
$P = 69~hp$
