A motorboat is traveling 5m/s East, and encounters a current traveling 2.5m/s, North. If the witdth of the river is 80m wide, how much time does it take the boat to reach the other shore. I understand how to calculate the resulatant velocity, but I don't understand why you use the velocity 5 m/s to calculate the time and not the resultant velocity, 5.59m/s to calculate the time.
remember the displacement (with velocity) is a vector equation.
displacementEast=velocityEast*time
To calculate the time it takes for the boat to reach the other shore, we need to consider the horizontal and vertical components separately.
First, let's calculate the time it takes for the boat to cross the river, which is the horizontal component of the motion. The boat is traveling to the east with a velocity of 5 m/s, and the width of the river is 80 m. Therefore, we can use the formula:
Time = Distance / Velocity
Time = 80 m / 5 m/s = 16 s
Now let's consider the vertical component of the motion. The boat encounters a current traveling north with a velocity of 2.5 m/s. However, this current does not affect the time it takes for the boat to cross the river because it only influences the boat's drift from its intended path but not its velocity in the eastward direction.
The resultant velocity of the boat, taking into account both the eastward motion and the northward drift, is 5.59 m/s, as you correctly mentioned. However, this resultant velocity is not used to calculate the time because it represents the boat's overall velocity in all directions combined.
Therefore, the time it takes for the boat to reach the other shore is only calculated based on its horizontal (eastward) velocity, which is 5 m/s in this case.