a canoe travels $31.0^\circ$ downstream from straight across a river. if the current pushes the boat downstream with a force of $5,120\text{ n}$, what is the net force on the boat?

$\bigcirc$ $9,140\text{ n}$
$\bigcirc$ $9,370\text{ n}$
$\bigcirc$ $9,940\text{ n}$
$\bigcirc$ $10,500\text{ n}$

Question

a canoe travels $31.0^\circ$ downstream from straight across a river. if the current pushes the boat downstream with a force of $5,120\text{ n}$, what is the net force on the boat?

$\bigcirc$ $9,140\text{ n}$
$\bigcirc$ $9,370\text{ n}$
$\bigcirc$ $9,940\text{ n}$
$\bigcirc$ $10,500\text{ n}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Right Triangle Geometry" ], "new_concepts": [ "Vector Resolution", "Net Force Calculation" ], "current_concepts": [ "Right Triangle Geometry", "Vector Resolution", "Net Force Calculation" ] } ## Identify the vector components Using the *Right Triangle Geometry* knowledge point $$ \begin{aligned} &\theta = 31.0^\circ\ &F_{\text{downstream}} = F_{\text{net}} \cdot \sin(\theta)\ &5,120\text{ N} = F_{\text{net}} \cdot \sin(31.0^\circ) \end{aligned} $$ ## Solve for the net force Using the *Right Triangle Geometry* knowledge point $$ \begin{aligned} &F_{\text{net}} = \frac{5,120\text{ N}}{\sin(31.0^\circ)}\ &\sin(31.0^\circ) \approx 0.515038\ &F_{\text{net}} \approx \frac{5,120}{0.515038} \approx 9,941\text{ N} \end{aligned} $$

(A) 9,140 N

(B) 9,370 N

(C) 9,940 N

(D) 10,500 N

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Question

Explanation:

Identify the vector components

Solve for the net force

Answer: