The stooping distance d of a car after the brakes are appied varies directly as the square root of the speed r. If a car traveling 40mph can stop in 90 ft., how many feet will it take the same car to stop when it is traveling 60 mph.

Question

The stooping distance d of a car after the brakes are appied varies directly as the square root of the speed r. If a car traveling 40mph can stop in 90 ft., how many feet will it take the same car to stop when it is traveling 60 mph.

Answer 1

d = kr^2

90 = 1600k
k = 9/160

d(60) = 9/160 * 3600 = 202.5

Answer 2

To solve this problem, we need to use the concept of direct variation and the given information.

First, let's set up the direct variation equation using the stooping distance (d) and the speed (r):

d = k * sqrt(r)

where k is the constant of variation.

We know that when the car is traveling at 40 mph, it can stop in 90 ft. Let's use this information to find the value of k:

90 = k * sqrt(40)

To find k, we isolate it by dividing both sides of the equation by sqrt(40):

k = 90 / sqrt(40)

Now that we have the value of k, let's use it to find the stooping distance (d) when the car is traveling at 60 mph:

d = k * sqrt(r)
d = (90 / sqrt(40)) * sqrt(60)

Now we can calculate the value of d:

d ≈ (90 / sqrt(40)) * sqrt(60)

Using a calculator, we find that:

d ≈ 127.28 ft

Therefore, it will take approximately 127.28 feet for the car to stop when traveling at 60 mph.

Answer 3

To solve this problem, we can use the concept of direct variation. Direct variation means that two variables are related such that when one variable increases or decreases, the other variable changes in proportion.

First, let's write the general equation for the relationship between the stooping distance (d) and speed (r) using direct variation:

d = kr^0.5

where k is the constant of variation.

To find the value of k in this specific scenario, we can use the given information: when the car is traveling at 40 mph (r = 40), the stooping distance is 90 ft (d = 90). Plugging these values into the equation, we have:

90 = k(40)^0.5

To solve for k, square both sides of the equation to eliminate the square root:

90^2 = k(40)

8100 = 40k

Now, divide both sides of the equation by 40:

k = 8100 / 40

k = 202.5

So, the constant of variation is k = 202.5.

Now that we have the value of k, we can use it to find the stooping distance (d) when the car is traveling at 60 mph (r = 60):

d = 202.5(60)^0.5

Calculating this, we get:

d = 202.5 * 7.745966692414834

d ≈ 1570.50

Therefore, when the car is traveling at 60 mph, it will take approximately 1570.50 ft for it to stop.