Story problems are my favorite. However, I can not figure this one out. THe stopping distance d of a car after the breaks are applied varies directly as the square of the speed r. If a car traveling at 70mph can stop in 270 ft. How many feet will it take the same car to stop when traveling at 90mph

distance=k*r^2

is the basic relationship. Take the 70/270f data, and solve for k.
then,
distance=k(90)^2

To solve this story problem, we can use the concept of direct variation and formulate an equation to find the stopping distance.

It is given that the stopping distance of a car varies directly as the square of the speed. So, we can write the equation as:

d = k * r^2

Where:
- d = stopping distance
- r = speed of the car
- k = constant of variation

Now, we need to find the value of k. For this, we can use the information provided in the problem. It states that when the car is traveling at 70 mph, the stopping distance is 270 ft.

Plugging in these values into the equation, we have:

270 = k * (70)^2

Simplifying:

270 = k * 4900

Now, we can solve for k by dividing both sides of the equation by 4900:

k = 270 / 4900
k = 0.0551 (rounded to four decimal places)

Now that we know the value of k, we can use it to find the stopping distance when the car is traveling at 90 mph. We'll plug in the new speed value into our equation:

d = 0.0551 * (90)^2

Simplifying:

d = 0.0551 * 8100

Calculating:

d ≈ 446.01 ft (rounded to two decimal places)

Therefore, when the car is traveling at 90 mph, it would take approximately 446.01 feet to stop.