A motorboat\'s bow is pointed due south, and its motor gives the boat a constant

Question

A motorboat's bow is pointed due south, and its motor gives the boat a constant speed of 5.00 m/s through still water. However, the water has a current flowing due east at a speed of 3.00 m/s.

A) Find the magnitude and direction of the boat's total velocity (relative to stationary objects along the shore.) Include a sketch of the two velocity vectora and their sum.

B) If the boat and water current maintain these same velocities for 50.0 seconds, find the magnitude and direction of the boat's displacement.

Explanation / Answer

here,

Vb = 5j m/s

Vr = 3i m/s

A)

Here,

Vbr = Vb + Vr

Vbr = 3i + 5j

| Vbr | = sqrt(3^2 + 5^2)

| Vbr | = 5.83 m/s

Theta = arctan(5/3)

theta = 59o

Velocity of magnitude is 5.83 m/s and it is  59o south of east .

B)

For time = 50 s

displacement = velocity * time

D = 50*(3i + 5j )

D = 150 i + 250j

| D | = 291.6 m

Theta = arctan(5/3)

theta = 59o

Displacement is 291.6 m and angle is 59o south of west

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