You are in a boat that is traveling across a river from east to west at 4.0 m/s. the river runs north at 3.0 m/s. what is the resultant velocity of the boat?
Vb = 4m/s @ 180o + 3m/s @ 90o.
X = 4*cos180 + 3*cos90 = -4 m/s.
Y = 4*sin180 + 3*sin90 = 3 m/2.
tanAr = Y/X = 3/-4 = -0.7500
Ar = 36.87o = Reference angle.
A = 180 - 36.87 = 143o.
Vb = X/cosA = -4/cos143 = 5 m/s.
To find the resultant velocity of the boat, we need to consider the velocities of the boat and the river separately and then combine them using vector addition.
The velocity of the boat relative to the ground is given as 4.0 m/s eastward. Let's denote this velocity as Vboat.
The velocity of the river is given as 3.0 m/s northward. However, we need to convert this velocity into an eastward component since the boat is traveling eastward.
To find the eastward component of the river's velocity, we can use trigonometry. The angle between the river's direction (north) and the eastward direction is 90 degrees. So, we can use the cosine function to find the eastward component of the river's velocity.
Eastward component of the river's velocity = River's velocity * cos(angle)
= 3.0 m/s * cos(90 degrees)
= 0 m/s
Now, we can combine the eastward velocity of the boat (4.0 m/s) with the eastward component of the river's velocity (0 m/s) using vector addition.
Resultant velocity of the boat = Vboat + Eastward component of river's velocity
= 4.0 m/s + 0 m/s
= 4.0 m/s
Therefore, the resultant velocity of the boat is 4.0 m/s eastward.