According to Car and Driver, an Alfa Romeo going 70 mph requires 177 feet to stop. Assuming that the stopping distance is proportional to the square of the velocity, find the stopping distance required by an Alfa Romeo going at 45 mph and at 115 mph.
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To find the stopping distance required by an Alfa Romeo going at 45 mph and 115 mph, we need to use the information given that the stopping distance is proportional to the square of the velocity.
Let's first find the proportionality constant. We have the following data:
Velocity (v1) = 70 mph
Stopping distance (d1) = 177 feet
Using the proportionality, we can write:
v1^2 / d1 = v2^2 / d2
where v2 is the velocity we want to find the stopping distance for, and d2 is the stopping distance.
Let's find the stopping distance for a velocity of 45 mph:
v2 = 45 mph
Plugging in the values, we have:
(70 mph)^2 / 177 feet = (45 mph)^2 / d2
Simplifying the equation:
(70^2 * d2) = (45^2 * 177)
Now we can solve for d2:
d2 = (45^2 * 177) / 70^2
Calculating the value:
d2 ≈ 161.357 feet
Therefore, an Alfa Romeo traveling at 45 mph requires approximately 161.357 feet to stop.
Now let's find the stopping distance for a velocity of 115 mph:
v2 = 115 mph
Plugging in the values, we have:
(70 mph)^2 / 177 feet = (115 mph)^2 / d2
Simplifying the equation:
(70^2 * d2) = (115^2 * 177)
Now we can solve for d2:
d2 = (115^2 * 177) / 70^2
Calculating the value:
d2 ≈ 491.162 feet
Therefore, an Alfa Romeo traveling at 115 mph requires approximately 491.162 feet to stop.
To find the stopping distances required by an Alfa Romeo going at 45 mph and 115 mph, we will use the proportionality between stopping distance and the square of the velocity.
According to Car and Driver, an Alfa Romeo going 70 mph requires 177 feet to stop. Let's call this stopping distance S70 and the velocity V70.
S70 = 177 feet
V70 = 70 mph
We can set up a proportion using the stopping distances and velocities:
(S70 / S45) = (V70^2 / V45^2) [1]
(S70 / S115) = (V70^2 / V115^2) [2]
Now we can solve for S45 and S115 using these two equations.
1. Solve for S45:
(S70 / S45) = (V70^2 / V45^2)
S45 = S70 * (V45^2 / V70^2)
S45 = 177 * (45^2 / 70^2)
S45 = 88 feet (approximately)
Therefore, an Alfa Romeo going 45 mph requires approximately 88 feet to stop.
2. Solve for S115:
(S70 / S115) = (V70^2 / V115^2)
S115 = S70 * (V115^2 / V70^2)
S115 = 177 * (115^2 / 70^2)
S115 = 408 feet (approximately)
Therefore, an Alfa Romeo going 115 mph requires approximately 408 feet to stop.