Question

boat #1 travels directly across a river from point a to point b, a distance of 100 m, as pictured. the river current moves at a speed of 5 m/s and the boat has velocity of 2 m/s directly up. how long will it take for boat #1 to cross the river? a 10 sec b 14.3 sec c 20 sec d 50 sec

Explanation:

Step1: Analyze the motion components

The boat's velocity across the river (perpendicular to the river - current direction) is \(v = 2m/s\), and the distance to cross the river (perpendicular distance) is \(d=100m\). The river - current velocity is parallel to the river banks and does not affect the time taken to cross the river (because motion in perpendicular directions are independent).

Step2: Use the formula \(t=\frac{d}{v}\)

We know that the formula for time \(t\) in one - dimensional motion (here, the motion perpendicular to the river current) is \(t=\frac{d}{v}\), where \(d\) is the distance and \(v\) is the velocity in the direction of the distance.
Substitute \(d = 100m\) and \(v=2m/s\) into the formula: \(t=\frac{100}{2}\)

Answer:

\(t = 50s\), so the answer is D. 50 sec.