two cyclists A and B start cycling at the same time from a certain point C. cyclist A is cycling at 45km/h in an easterly direction. cyclist B is cycling north at 21km/h. find the shortest distance between the two hours. round answer off to two decimal places

Answer 1

To find the shortest distance between the two cyclists, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the right triangle are the distance travelled by cyclist A and cyclist B. Since the time is the same for both cyclists, the distance travelled by cyclist A after time t will be equal to the speed of cyclist A multiplied by t. Similarly, the distance travelled by cyclist B after time t will be equal to the speed of cyclist B multiplied by t.

Let's assume that the time elapsed is t hours.

Distance travelled by cyclist A = 45 * t (in km)
Distance travelled by cyclist B = 21 * t (in km)

Using the Pythagorean theorem, the square of the shortest distance between the two cyclists is equal to the sum of the squares of the distances travelled by each cyclist:

(45t)^2 + (21t)^2 = shortest distance^2

2025t^2 + 441t^2 = shortest distance^2

2466t^2 = shortest distance^2

Taking the square root of both sides:

shortest distance = sqrt(2466t^2)

Now, we need to find the value of t that gives us the shortest distance. Since we want to find the shortest distance, we can assume that the two cyclists have travelled for the same amount of time. Therefore, t is the same for both cyclists.

To find the shortest distance, we can substitute t = 1 into the equation:

shortest distance = sqrt(2466 * 1^2) = sqrt(2466)

Rounded off to two decimal places, the shortest distance between the two cyclists is approximately 49.66 km.