Respuesta :
Answer:
The car requires 192 feet to stop from a speed of 48 miles per hour on the same road
Step-by-step explanation:
- Direct proportion means that two quantities increase or decrease in the same ratio
- If y is directly proportional to x (y ∝ x) , then [tex]\frac{y_{1}}{y_{2}}=\frac{x_{1}}{x_{2}}[/tex] OR y = k x, where k is the constant of proportionality
∵ The stopping distance d of an automobile is directly
proportional to the square of its speed s
- That means d ∝ s²
∴ [tex]\frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}[/tex]
∵ A car requires 75 feet to stop from a speed of 30 miles per hour
∴ d = 75 feet
∴ s = 30 miles/hour
- Change the mile to feet
∵ 1 mile = 5280 feet
∴ 30 miles/hour = 30 × 5280 = 158400 feet/hour
∵ The car require to stop from a speed of 48 miles per hour
on the same road
- Change the mile to feet
∴ 48 miles/hour = 48 × 5280 = 253440 feet/hour
∵ [tex]\frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}[/tex]
- Substitute the values of [tex]d_{1}[/tex] by 75 feet, [tex]s_{1}[/tex] by 158400 feet/hour
and [tex]s_{2}[/tex] by 253440 feet/hour
∴ [tex]\frac{75}{d_{2}}=\frac{(158400)^{2}}{(253440)^{2}}[/tex]
∴ [tex]\frac{75}{d_{2}}=\frac{25}{64}[/tex]
- By using cross multiplication
∴ 25 × [tex]d_{2}[/tex] = 75 × 64
- Divide both sides by 25
∴ [tex]d_{2}[/tex] = 192 feet
The car requires 192 feet to stop from a speed of 48 miles per hour on the same road
The car require 192 feet to stop from a speed of 48 miles per hour.
Stopping distance:
It is given that, stopping distance d of an automobile is directly proportional to the square of its speed s.
So that, [tex]d=ks^{2}[/tex]
Where k is proportionality constant.
Since, a car requires 75 feet to stop from a speed of 30 miles per hour.
[tex]75=k(30)^{2} \\\\k=\frac{75}{900}=\frac{1}{12}[/tex]
We have to find stopping distance when speed is 48 miles per hour.
[tex]d=\frac{1}{12} *48*48\\\\d=48*4=192feet[/tex]
Hence, the car require 192 feet to stop from a speed of 48 miles per hour.
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