Assume that stopping distance of a van varies directly with the square of the speed. A van traveling 40 miles per hour can stop in 60 feet. If the van is traveling 68 miles per hour, what is the stopping distance?
60 * (68/40)^2
To solve this problem, we need to use the concept of direct variation. When two variables are said to vary directly, it means that one variable is directly proportional to the other. In this case, the stopping distance of the van is directly proportional to the square of the speed.
Let's denote the stopping distance as 'd' and the speed as 's'. According to the problem, we know that when the van is traveling at 40 miles per hour (s = 40), the stopping distance is 60 feet (d = 60).
Using the concept of direct variation, we can form the following equation:
d = k * s^2
Where 'k' is the constant of variation.
To find the value of 'k', we can substitute the known values into the equation:
60 = k * (40)^2
Simplifying the equation:
60 = 1600k
To solve for 'k', divide both sides of the equation by 1600:
k = 60/1600 = 0.0375
Now that we have the value of 'k', we can use it to find the stopping distance when the van is traveling at 68 miles per hour.
d = 0.0375 * (68)^2
Calculating the value:
d = 0.0375 * 4624
d ≈ 173.4
Therefore, when the van is traveling at 68 miles per hour, the approximate stopping distance is 173.4 feet.