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Answer:
1) 18.92°
2) 1480 m or 1.48 km
3) 40 s
Step-by-step explanation:
We can find the answers for a boat which travels at 37 m/s in a river that flows in a speed of 12 m/s by this way:
In order the boat travels in a perpendicular direction, the resultant of speed with respect to the flow's direction has to be equal to 0 (refer to the drawing), therefore the speed of the boat in x direction [tex](v_x)[/tex] equals to -12 m/s. We can find the angle (θ) by using the trigonometric formula:
1)
[tex]\begin{aligned}sin\theta&=\frac{|v_x|}{|v|} \\\\sin\theta&=\frac{12}{37} \\\\\theta&=asin\left(\frac{12}{37} \right)\\\\\theta&\approx\bf 18.92^o\end{aligned}[/tex]
2)
Since the distance in y direction [tex](s_y)[/tex], which is the river's width, is 1.4 km = 1400 m, then we can find the distance [tex](s)[/tex] by using the trigonometric formula:
[tex]\begin{aligned}cos\theta&=\frac{s_y}{s} \\\\cos(18.92^o)&=\frac{1400}{s} \\\\s&=\frac{1400}{cos(18.92)}\\\\s&=\bf 1480\ m\ or\ 1.48\ km\end{aligned}[/tex]
3) To find the time taken by the boat, we can use the linear motion with constant speed formula:
[tex]\boxed{s=vt}[/tex]
Given:
Then:
[tex]\begin{aligned}\\s&=vt\\1480&=37t\\t&=1480\div37\\t&=\bf40\ s\end{aligned}[/tex]
