a boat traveling at 3.0 m/s through the water keeps its bow pointing north across a stream that flows west…
a boat traveling at 3.0 m/s through the water keeps its bow pointing north across a stream that flows west at 5.0 m/s. what is the resultant velocity of the boat with respect to the shore?
Answer
Explanation:
Step1: Identify the velocities as vectors
The boat's velocity across the stream $v_y = 3.0\ m/s$ (north - positive y - direction) and the stream's velocity $v_x=- 5.0\ m/s$ (west - negative x - direction).
Step2: Use the Pythagorean theorem for resultant velocity
The magnitude of the resultant velocity $v$ of two perpendicular vectors $v_x$ and $v_y$ is given by $v=\sqrt{v_x^{2}+v_y^{2}}$. Substitute $v_x = - 5.0\ m/s$ and $v_y = 3.0\ m/s$ into the formula: [ \begin{align*} v&=\sqrt{(-5.0)^{2}+(3.0)^{2}}\ &=\sqrt{25 + 9}\ &=\sqrt{34}\ &\approx5.8\ m/s \end{align*} ]
Answer:
$5.8\ m/s$