Answer:
The car is 72.75 miles away from its starting position.
Explanation:
First, remember the relation:
distance = time*speed.
Also, the distance between two points (a, b) and (c, d) is:
D = √( (a - c)^2 + (b - d)^2)
For this problem, we can assume:
The North is equivalent to the y-axis, and the East is equivalent to the x-axis.
We also assume that the initial position of the car is (0mi, 0mi)
Now the car moves to the East at a speed of 52mi/h for one hour, then the new position of the car is:
(0mi, 0mi) + (52mi/h*1h, 0mi) = (52mi, 0mi)
Now the car travels 30 mins (or 0.5 hours) to the northeast at a speed of 52mi/h.
We can assume that it moves at an exact angle of 45° from East to North, then the components of the speed can be written as:
Sx = speed in the x-axis = 52mi/h*cos(45°) = 36.77 mi/h
Sy = speed in the y-axis = 52mi/h*sin(45°) = 36.77 mi/h
Then the new position of the car is:
(52mi, 0mi) + (36.77 mi/h*0.5h, 36.77 mi/h*0.5h) = (70.385 mi, 18.385 mi)
Now we know the final position of the car.
The distance between the final position (70.385 mi, 18.385 mi) and the initial position (0mi, 0mi) is:
D = √( (70.385 mi - 0mi)^2 + (18.385 mi - 0mi)^2) = 72.75 mi
The car is 72.75 miles away from its starting position.
