Question

A steamboat is traveling 3.3 m/s East and encounters a mysterious current traveling 3.5 m/s North. What is the resultant velocity? How long will it take the boat to reach shore if the river is .4 km long? At what distance downstream does it reach the opposite shore?​

Answer 1

The resultant velocity is 4.8 m/s. It will take 83.3 seconds for the boat to reach the shore, and it will reach the opposite shore at a distance downstream of 291.6 m.

Step-by-step explanation:

To find the resultant velocity, we can use the Pythagorean theorem because the boat's velocity and the current's velocity form a right triangle. The magnitude of the resultant velocity is given by:

Vresultant = sqrt((Vboat)^2 + (Vcurrent)^2)

Substituting the values, Vboat = 3.3 m/s and Vcurrent = 3.5 m/s, we get:

Vresultant = sqrt((3.3 m/s)^2 + (3.5 m/s)^2) = 4.8 m/s

To find the time it takes for the boat to reach shore, we can use the formula:

Time = Distance / Velocity

Substituting the values, Distance = 0.4 km and Velocity = 4.8 m/s, we need to convert the distance to meters:

Distance = 0.4 km imes 1000 m/km = 400 m

Time = 400 m / 4.8 m/s = 83.3 s

The boat will reach the opposite shore at a distance downstream equal to the velocity of the river multiplied by the time it takes to cross the river:

Distance downstream = Vcurrent imes Time = 3.5 m/s imes 83.3 s = 291.6 m