Multiple choice

A car starts to go the west at 30 km/hr and another car starts to go the north at 40 km/hr at time t = 0. The distance between them at any time t (in hours) is given by

  1. 10 t

  2. 40 t

  3. 50 t

  4. 70 t
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C Correct answer
Explanation

The cars move in perpendicular directions (West and North). The distance between them at time t forms the hypotenuse of a right triangle with legs 30t and 40t. Distance = sqrt((30t)^2 + (40t)^2) = sqrt(900t^2 + 1600t^2) = sqrt(2500t^2) = 50t.

AI explanation

The two cars are moving in perpendicular directions, west and north, so the distance between them forms the hypotenuse of a right-angled triangle. Using the Pythagorean theorem, the distance is the square root of the sum of the squares of their individual distances, which are 30t and 40t. This gives the square root of (30t)^2 + (40t)^2, equaling the square root of 900t^2 + 1600t^2, which simplifies to 50t.

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