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

319 seconds

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