Police use a formula s = S √1/L , where S is the test-car speed and L is the test-skid length, to find the actual speed s in an accident which left a skid mark of l. Find the actual speed s (nearest whole mph) when S=45 mph, 1=150 ft, L=100 ft.
l and 1 are too confusing.
I will use x for theunknown skid length
s^2 = S^2 (x/L)
s^2 = 45^2 (1.5) = 3037.5
s = 55.1
Well, let's crunch some numbers while trying to keep the laughter going!
First, let's calculate L - Sqrt(l):
L = 100 ft
l = 150 ft
So, L - Sqrt(l) = 100 - Sqrt(150) ≈ 91.02 ft
Now, let's plug in the values:
s = S √1/L = 45 mph * √1/91.02 ft = 45 mph * 0.316 mph/ft ≈ 14.22 mph
So, based on my calculations, the actual speed s (rounded to the nearest whole mph) is approximately 14 mph. But note that this is just an estimation, so take it with a grain of humor!
To find the actual speed, s, using the given formula s = S √(1/L), where S is the test-car speed and L is the test-skid length, we need to substitute the provided values into the formula and solve for s.
Given:
S = 45 mph
L = 100 ft
l = 150 ft
Let's substitute these values into the formula:
s = 45 mph √(1/100)
Next, we can simplify the expression inside the square root:
s = 45 mph √0.01
Taking the square root of 0.01:
s = 45 mph * 0.1
Now, we can multiply the car speed by 0.1:
s = 4.5 mph
Therefore, the actual speed, s, when S = 45 mph, L = 100 ft, and l = 150 ft, is approximately 4.5 mph.
To find the actual speed s using the given formula, we need to substitute the values of S, L, and l into the formula and solve for s. Here's how we can do that:
Step 1: Substitute the values into the formula:
s = S * sqrt(1 / L)
Given values: S = 45 mph, L = 100 ft, l = 150 ft
Substituting the values:
s = 45 * sqrt(1 / 100)
Step 2: Simplify the equation:
s = 45 * sqrt(0.01)
Step 3: Calculate the square root:
s = 45 * 0.1
s = 4.5 mph
Therefore, the actual speed s of the test car, when S = 45 mph, L = 100 ft, and the skid length l = 150 ft, is approximately 4.5 mph when rounded to the nearest whole mph.