Car A is moving due east at 80 km/h. Car B, 8 km to the east, is moving due south at 50 km/h. Calculate the shortest distance between A and B?

Answer 1

We can solve this problem using the Pythagorean theorem to find the shortest distance between Car A and Car B.

Let's define the positions of Car A and Car B as points A and B respectively. Let the points where Car A and Car B meet be M and N respectively. We can form a right triangle by connecting points A, B, M, and N.

The distance between A and M = 80 km/h * t (where t is the time taken to reach point M)
The distance between B and N = 50 km/h * t (where t is the time taken to reach point N)

Since A and B are 8 km apart horizontally, the distance between M and N would be 8 km.

Applying the Pythagorean theorem:
(80t)^2 + (50t)^2 = 8^2
6400t^2 + 2500t^2 = 64
8900t^2 = 64
t^2 = 64 / 8900
t ≈ 0.071

Substitute t into one of the distance formulas to find the minimum distance between Car A and Car B:
80 * 0.071 ≈ 5.68 km

Therefore, the shortest distance between Car A and Car B is approximately 5.68 km.