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# Answer to Question #108855 in Mechanics | Relativity for Cindy

Question #108855
A motor boat is heading due north and crosses a wide river with a speed of 4m/s relative to the water. the water in the river has a uniform speed of 3m/s due east relative to the earth . determine the direction of the motion of the motor boat relative to the earth
1
2020-04-10T08:51:28-0400

Notations

• Velocity of the boat relative to the river: V(b.r)
• Velocity of the river relative to earth v(r,e)
• Velocity of the boat relative to earth: V(b,e)
• Angle between V(b,e) & V(r,e) velocity vectors "\\theta"

Calculations

• Considering the vector triangle which could be formed by all the velocity vectors the boat is exposed to (Refer the sketch attached),

"\\qquad\n\\begin{aligned}\n\\small \n\\end{aligned}" "\\qquad\n\\begin{aligned}\n\\small \\tan{\\theta}&=\\small \\frac{V_{b,r}}{V_{r,e}}\\\\\n\\small \\theta&= \\small \\tan^{-1}(\\frac{4\\,ms^{-1}}{3\\,{ms^{-1}}})\\\\\n\\small &= \\small \\bold{53.13^{\\degree}} \n\\end{aligned}"

Therefor, the direction of the boat is "\\small \\bold {53.13^{\\degree}}" to north from east.

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