A boat moves with a velocity of 15 m/s, north in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north
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To calculate the boat's resultant velocity with respect to due north, we can use vector addition.
The velocity of the boat can be represented as a vector pointing due north with a magnitude of 15 m/s:
Boat velocity = 15 m/s, north
The velocity of the river can be represented as a vector pointing due west with a magnitude of 8.0 m/s:
River velocity = 8.0 m/s, west
To find the resultant velocity, we need to add these two vectors together. Since the velocities are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant velocity:
Resultant velocity = sqrt((Boat velocity)^2 + (River velocity)^2)
Using the given values:
Resultant velocity = sqrt((15 m/s)^2 + (8.0 m/s)^2)
Calculating:
Resultant velocity = sqrt(225 m^2/s^2 + 64 m^2/s^2)
Resultant velocity = sqrt(289 m^2/s^2)
Resultant velocity = 17 m/s
Therefore, the boat's resultant velocity with respect to due north is 17 m/s.
To calculate the resultant velocity of the boat with respect to due north, we can use vector addition.
In this scenario, the velocity of the boat is given as 15 m/s, north, and the velocity of the river is given as 8.0 m/s, west.
Step 1: Represent the velocities as vectors.
The velocity of the boat can be represented as a vector pointing north, with a magnitude of 15 m/s. Let's call this vector B.
The velocity of the river can be represented as a vector pointing west, with a magnitude of 8.0 m/s. Let's call this vector R.
Step 2: Find the vector sum.
To find the resultant velocity, we need to add the vectors B and R. Since these vectors are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant velocity.
Magnitude of resultant velocity (V) = √(15^2 + 8.0^2)
Step 3: Determine the direction.
To determine the direction of the resultant velocity, we can use trigonometric functions. In this case, we need to find the angle between the resultant velocity and the north direction.
Angle (θ) = arctan(8.0/15)
Therefore, the boat's resultant velocity with respect to due north is V = √(15^2 + 8.0^2) m/s, at an angle of θ = arctan(8.0/15) with respect to north.
v = √(15^2 + 8^2)
Θ is the direction angle west of north
... tan (Θ) = 8 / 15