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Huck Finn walks at a speed of 0.70 m/sm/s across his raft (that is, he walks perpendicular to the raft's motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.60 m/sm/s relative to the river bank. What is Huck's velocity (speed and direction) relative to the river bank?

Answer :

Answer:

Explanation:

Given

Velocity of Huck w.r.t to raft [tex]v_{H,raft}=0.7\ m/s[/tex]

Perpendicular to the motion of raft

Velocity of Raft in the river [tex]v_{raft,river}=1.6\ m/s[/tex]

As Huck is traveling Perpendicular to the raft so he possess two velocities i.e. vertical velocity and horizontal velocity of River when observed from bank

[tex]v_{Huck,river\ bank}=0.7\hat{j}+1.6\hat{i}[/tex]

So magnitude of velocity is given by

[tex]|v|=\sqrt{0.7^2+1.6^2}[/tex]

[tex]|v|=\sqrt{0.49+2.56}[/tex]

[tex]|v|=\sqrt{3.05}[/tex]

[tex]|v|=1.74\ m/s[/tex]

For direction [tex]\tan =\frac{0.7}{1.6}=0.4375[/tex]

[tex]\theta =23.63^{\circ}[/tex] w.r.t river bank

                       

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