Multiple choice

A boat is moving from the east bank to the west bank on a south 'flowing river. The speed of the boat is 4 km/h and that of the river is 3 km/h. If the width of the river is 2 km, the distance travelled by the boat is

  1. 5 km

  2. 4 km

  3. 3 km

  4. 2.5 km

  5. 2 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The boat travels across the river (width 2 km). The resultant velocity is the vector sum of the boat speed (4 km/h) and river speed (3 km/h). The time taken to cross is 2/4 = 0.5 hours. In this time, the boat drifts downstream, but the question asks for the distance travelled by the boat relative to the ground, which is sqrt(4^2 + 3^2) * 0.5 = 5 * 0.5 = 2.5 km.

AI explanation

Using the method of vector addition for the boat's velocity, the actual speed of the boat is the square root of (4 squared plus 3 squared), which equals 5 km/h. The time taken to cross the 2 km wide river is calculated by dividing the width by the westward component of the speed, giving 2 divided by 4, or 0.5 hours. Using the formula Distance = Speed multiplied by Time, the total distance traveled by the boat is 5 km/h multiplied by 0.5 hours, resulting in 2.5 km.

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