Question

How long would it take a car with a top speed of 203 mph to travel 12.42 miles up a slope of 6.4% accelerating at 0.091 G's (2.93 ft/s sq.)

Answer 1

Answer:

319 seconds

Step-by-step explanation:

The distance 12.42 miles is equivalent to

12.42*5280=65577.6 ft

$ma-mgsin\theta=ma_{net}$

When slope is 6.4%, $\theta=tan^{-1} 0.064=3.67^{\circ}$

$a_{net}=a-gsin\theta=2.93-32.2sin3.67=-0.87$

Therefore, $a_{net}=-0.87 ft/s^{2}$

Also

$s=ut+0.5a_{net}$

$65577.6=297.73t+0.5(-0.87)t^{2}$

$0.87t^{2}-297.73t+6577.6=0$

Making t the subject of the formula by solving quadratic equation

t=318.4791278210496

Therefore, time is 319 seconds