Distances

A boy is rowing a boat at a speed of 7.2 km/h. He directed the boat perpendicularly to the opposite bank, which is 600 m away. The river carries the boat at a speed of 4.0 km/h. What is the resulting speed of the boat relative to the bank? How far will the river carry the boat from where the boat should land? How far from the starting point will the boat land?

Correct answer:

v =  8.2365 km/h
s₁ =  0.3333 km
x =  0.6864 km

Step-by-step explanation:

$$\begin{gathered} v_1=7.2 \\ {v}_2=4.0 \\ l=600/1000=\frac{3}{5}=0.6 \\ v=\sqrt{v_1^2+v_2^2}=\sqrt{7.2^2+4^2}=8.2365\text{km/h} \end{gathered}$$

$$\begin{gathered} t_1=l/v_1=0.6/7.2=\frac{1}{12}\doteq 0.0833 \\ {s}_1=t_1\cdot v_2=0.0833\cdot 4=0.3333\text{km} \end{gathered}$$

$x=\sqrt{s_1^2+l^2}=\sqrt{0.3333^2+0.6^2}=0.6864\text{km}$

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