A boat moves with a velocity of 15m/s north in a river, which flows with a velocity of 8m/ s west. Calculate the boat resistant velocity with respect due to North.

A boat moves with a velocity of 15m/s north in a river, which flows with a velocity of 8m/ s west. Calculate the boat resistant velocity with respect due to North.

resultant, not resistant.

It will be θ west of north, with tanθ = 8/15
and of course, you recognize an 8-15-17 triangle, right?

Why did the boat go to a therapist?

Because it had issues with its resistance!

To calculate the boat's resultant velocity with respect to the north, we can use the Pythagorean theorem. The boat's velocity can be broken down into two components: one in the north direction and one in the west direction. The resulting velocity can be calculated as follows:

Resultant velocity = √(velocity north^2 + velocity west^2)

Given that the velocity north is 15 m/s and the velocity west is 8 m/s, we can plug these values into the formula:

Resultant velocity = √(15^2 + 8^2)
= √(225 + 64)
= √289
= 17 m/s

So, the boat's resultant velocity with respect to the north is 17 m/s.

To calculate the boat's resultant velocity with respect to the north, we can use vector addition. The boat's velocity and the river's velocity are vectors that need to be added together.

Given:
Boat velocity in the north direction (Vb, N) = 15 m/s
River velocity in the west direction (Vr, W) = 8 m/s

To find the boat's resultant velocity with respect to the north, we need to find the vector sum of the boat's velocity and the river's velocity. Since the two velocities are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant velocity and trigonometry to find its direction.

1. Magnitude of Resultant Velocity:
Using the Pythagorean theorem,
Resultant velocity magnitude (Vr) = sqrt((Vb)^2 + (Vr)^2)
= sqrt((15)^2 + (8)^2)
= sqrt(225 + 64)
= sqrt(289)
= 17 m/s (rounded to one decimal place)

2. Direction of Resultant Velocity:
Using trigonometry, specifically the tangent function,
Resultant velocity direction (theta) = arctan(Vb / Vr)
= arctan(15 / 8)
≈ 60.26° (rounded to two decimal places)

Therefore, the boat's resultant velocity with respect to the north is approximately 17 m/s at an angle of 60.26° north of west.

7m/s