A boat is heading due north across a river with a speed of 12.0 km/h relative to the water. The water in the river has a uniform velocity of 6.00 km/h due east relative to the ground. Determine the velocity of the boat relative to an observer standing on either bank.

Respuesta :

The velocity of the boat relative to an observer standing on either bank = u = 18 [tex]\frac{km}{hr}[/tex]

Explanation:

Let speed of the boat in still water = u [tex]\frac{km}{hr}[/tex]

speed of the river water = v [tex]\frac{km}{hr}[/tex]

Relative speed of the boat in the water against the river flow is given by

Upstream speed = u - v ------- (1)

⇒ u - v = 12 [tex]\frac{km}{hr}[/tex] ------ (2)

Given that speed of the water = 6 [tex]\frac{km}{hr}[/tex]

Now velocity of the boat is given From equation (2)

⇒ u = 12 + v

Put the value of v = 6 , we get

⇒ u = 12 + 6

⇒ u =  18 [tex]\frac{km}{hr}[/tex]

therefore , the velocity of the boat relative to an observer standing on either bank = u = 18 [tex]\frac{km}{hr}[/tex]