A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely in 6s?
(30 + 14)/6 = speed
Convert from feet per second to mph.
I hope this helps.
let the speed of car =xmi/h
relative speed =(x-50)mi/h
time taken to overtake=1/600h
s=d/t
distance to be covered=44/5280mi
s*t=d
(x-50)(1/600)=44/5280
x=55mi/h
To find the speed at which the woman must drive her car to pass the truck completely in 6 seconds, we need to calculate the relative speed between the car and the truck.
Step 1: Convert the length of the car and truck to the same unit.
Since the truck is 30 ft long and the car is 14 ft long, we can work with feet for this calculation.
Step 2: Convert the given time to hours.
The given time is 6 seconds. Since we need to work with the speed in miles per hour, we need to convert this time to hours. There are 60 seconds in a minute and 60 minutes in an hour, so 6 seconds is equal to 6/3600 hours.
Step 3: Calculate the relative speed.
To pass the truck completely, the car must cover its own length plus the truck's length in the given time. This means the relative speed between the car and the truck during this time is:
Relative speed = (Car length + Truck length)/Time
Relative speed = (14 ft + 30 ft)/(6/3600 hrs) = (44 ft)/(1/600 hrs) = 44 * 600 ft/hour
Step 4: Convert the relative speed to miles per hour.
There are 5280 feet in a mile and 1 hour is equal to 60 minutes. Therefore, we can convert the relative speed from feet per hour to miles per hour:
Relative speed = (44 * 600 ft/hour) / (5280 ft/mi) = (44 * 600) / (5280) mi/h
Relative speed = 5 mi/h
Therefore, the woman must drive her car at a speed of 5 miles per hour to pass the truck completely in 6 seconds.
To determine the speed at which the woman must drive her car to pass the truck, we need to find the distance that needs to be covered in 6 seconds.
First, we need to calculate the combined length of the car and the truck:
Combined length = Length of car + Length of truck
Combined length = 14 ft + 30 ft
Combined length = 44 ft
Since the car needs to pass the truck completely, it needs to travel a distance equal to the combined length. In this case, it needs to cover 44 ft.
Now, we need to convert the time given into seconds, as the unit for speed is typically measured in feet per second. Therefore, we have:
Time = 6 seconds
To find the required speed, we use the formula: Speed = Distance / Time
Speed = 44 ft / 6 s
Speed ≈ 7.33 ft/s
Therefore, the woman must drive her car at a speed of approximately 7.33 feet per second to pass the truck completely in 6 seconds.