A jeep is traveling in a straight line across a flat, empty dessert. On a navigational map with a unit representing 1 km, the starting point of the jeep is at (-140, -70) and its destination is at (280,50). There is a refueling depot with an emergency transmitter half way along the route. During the journey, the jeep shows signs that engine trouble will soon develope. The driver must decide whether to turn back to the start, or try for the refueling depot, or continue to the end of the trip. If the jeep travels at 30km/h what should the driver do in each of the follwing situations. Explain.
A)the signs of engine trouble devlop after 4 hours
B) The signs of engine trouble develop after 11 hours
please help!!
a) keep going 98.4 km left
To determine what the driver should do in each situation, we need to calculate the distances involved and compare them to the estimated time it would take the driver to reach each location.
First, let's calculate the distances between the starting point, the refueling depot, and the destination:
Distance between starting point and refueling depot:
- x-distance = 280 - (-140) = 420 km
- y-distance = 50 - (-70) = 120 km
Using the Pythagorean theorem, we can calculate the total distance between the starting point and the refueling depot:
- distance = sqrt(420^2 + 120^2) = sqrt(176,400 + 14,400) = sqrt(190,800) ≈ 436.75 km
Distance between refueling depot and destination:
- x-distance = 280 - 140 = 140 km
- y-distance = 50 - (-70) = 120 km
Again, using the Pythagorean theorem, we can calculate the total distance between the refueling depot and the destination:
- distance = sqrt(140^2 + 120^2) = sqrt(19,600 + 14,400) = sqrt(34,000) ≈ 184.39 km
Now, let's consider each situation:
A) The signs of engine trouble develop after 4 hours:
- At a speed of 30 km/h, the jeep would have traveled a distance of 4 * 30 = 120 km.
- Since the distance to the refueling depot is approximately 436.75 km, the driver should continue to the refueling depot as this is closer than turning back to the starting point or continuing to the destination.
B) The signs of engine trouble develop after 11 hours:
- At a speed of 30 km/h, the jeep would have traveled a distance of 11 * 30 = 330 km.
- Since the distance to the refueling depot is approximately 436.75 km, the driver should continue to the refueling depot as it is closer than the destination and they may run out of fuel before reaching the destination.
In both situations, the best course of action is to head towards the refueling depot because it is closer than both the starting point and the destination.