Two roads intersect at an angle of 48º. A car and truck collide at the
intersection, and then leave the scene of the accident. The car travels at
100 km h down one road, while the truck goes 80 km h down the other road.
Fifteen minutes after the accident, a police helicopter locates the car and pulls it over. Twenty minutes after the accident, a police cruiser pulls over the truck. How far
apart are the car and the truck at this time?
To find the distance between the car and truck, we first need to calculate the distance each vehicle has traveled during the time interval.
Let's consider the car first:
Speed = 100 km/h
Time = 15 minutes = 15/60 hours = 0.25 hours
Distance traveled by the car = Speed * Time = 100 km/h * 0.25 hours = 25 km
Now, let's consider the truck:
Speed = 80 km/h
Time = 20 minutes = 20/60 hours = 0.33 hours
Distance traveled by the truck = Speed * Time = 80 km/h * 0.33 hours = 26.4 km
So, at this time, the car and truck are approximately 25 km + 26.4 km = 51.4 km apart.
To find how far apart the car and the truck are at this time, we need to determine the distance each vehicle has traveled since the accident occurred.
Given:
- Car speed: 100 km/h
- Truck speed: 80 km/h
- Time elapsed for the car: 15 minutes
- Time elapsed for the truck: 20 minutes
First, let's convert the time elapsed for both vehicles into hours to match their speeds:
- Time elapsed for the car: 15 minutes = 15/60 = 0.25 hours
- Time elapsed for the truck: 20 minutes = 20/60 = 0.33 hours
Now, we can calculate the distance each vehicle has traveled using the formula:
Distance = Speed × Time
For the car:
Distance car = 100 km/h × 0.25 hours
Distance car = 25 km
For the truck:
Distance truck = 80 km/h × 0.33 hours
Distance truck = 26.4 km (rounded to one decimal place)
Therefore, the car and the truck are approximately 25 km and 26.4 km apart, respectively, at this time.
Same cosine law as I just showed you.
Except in this case you have to calculate the lengths of the two sides.
But that is easy, aren't you given the time and speed?
Remember distance = time x speed.