The fastest time ever run at pikes peak is 7: 57. that’s way too long. if we removed all the curves, making a straight line from top to bottom, how quickly could a car reach the top?
protips:
slope of 6.4%
car top speed 203 mph
a stock car has a peak acceleration of over 1g. assume this car will accelerate at an average of .091 g (2.93 ft/s2)
the 12.42 mile long pike’s peak course has over 156 turns

271.4 s

Explanation:

We are told the top speed (maximum speed) the car has is:

taking into account

And the car's average acceleration is:

Since:

(1)

Where:

is the car's final speed (top speed)

because it starts from rest

is the time it takes to reach the top speed

Finding this time:

(2)

(3)

(4)

Now we have to find the distance the car traveled at this maximum speed with the following equation:

(5)

Isolating :

(6)

(7)

(8)

On the other hand, we know the total distance traveled by the car is:

Hence the remaining distance is:

(9)

(10)

So, we can calculate the time it took to this car to travel this remaining distance at its top speed , with the following equation:

(11)

Isolating :

(12)

(13)

(14)

With this time and the value of calculated in (4) we can finally calculate the total time :

(15)

(16)

the answer is b, have negligible mass

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min