Two cars are driving toward each other on a straight and level road in Alaska. The BMW is traveling at 115 km/h north and the VW is traveling at 54.0 km/h south, both velocities measured relative to the road. At a certain instant, the distance between the cars is 11.6 km. Approximately how long will it take from that instant for the two cars to meet?
Relative velocity is
115+54 = 169 km/h.
t=s/V(rel) =11.6/169=0.068 h=4.12 min
To calculate the time it will take for the two cars to meet, you need to first determine their relative velocity. Since one car is traveling north and the other is traveling south, their velocities will be additive.
First, convert the velocities to the same units. We'll use km/h for consistency.
The BMW is traveling at 115 km/h north, so its velocity is +115 km/h.
The VW is traveling at 54.0 km/h south, so its velocity is -54.0 km/h.
To find the relative velocity, add the two velocities together:
Relative velocity = 115 km/h + (-54.0 km/h)
Relative velocity = 61.0 km/h
Now that we know the relative velocity, we can use it to calculate the time it will take for the two cars to meet. Use the formula:
Distance = Relative velocity * Time
In this case, the distance is given as 11.6 km. Plugging in the values, we get:
11.6 km = 61.0 km/h * Time
To find Time, divide both sides of the equation by 61.0 km/h:
Time = 11.6 km / 61.0 km/h
Calculating this, we have:
Time = 0.19 hours
Since the question asks for an approximate time, we can round it to the nearest decimal place. Therefore, it will take approximately 0.2 hours for the two cars to meet.