A boat is heading due north as it crosses a wide river with a velocity of 10km/hr relative to the water.the river has a velocity of 5km due east determine the velocity of the boat with respect on the river bank
Well, if the boat is heading due north and the river has a velocity due east, it seems like the boat is going to have a little trouble finding its way to the river bank. It might end up doing some unexpected river-dance moves!
But let's crunch some numbers! To determine the velocity of the boat with respect to the river bank, we can use good old Pythagoras. The boat's velocity is like the hypotenuse of a right triangle, with the velocity due north as one side and the velocity due east as the other side. Using the Pythagorean theorem, we can calculate it:
Velocity of the boat = √(velocity due north)^2 + (velocity due east)^2
Velocity of the boat = √(10 km/hr)^2 + (5 km/hr)^2
Velocity of the boat = √(100 km^2/hr^2) + (25 km^2/hr^2)
Velocity of the boat = √125 km^2/hr^2
Velocity of the boat = 11.18 km/hr (rounded to two decimal places)
So there you have it! The velocity of the boat with respect to the river bank is approximately 11.18 km/hr. Enough to keep the boat moving, but let's hope the captain has a sense of direction or a GPS handy!
To determine the velocity of the boat with respect to the river bank, we need to use vector addition.
Let's call the velocity of the boat with respect to the river bank "V". From the information given, we know that the boat has a velocity of 10 km/hr due north relative to the water, and the river has a velocity of 5 km/hr due east.
Using vector addition, we can find the resultant velocity of the boat:
V = Boat's velocity relative to the water + River's velocity
V = 10 km/hr north + 5 km/hr east
Since the velocities are at right angles to each other, we can treat them as perpendicular components of a right-angled triangle. We can use the Pythagorean theorem to find the magnitude of the resultant velocity:
V = sqrt((10^2) + (5^2))
V = sqrt(100 + 25)
V = sqrt(125) km/hr
So, the velocity of the boat with respect to the river bank is approximately 11.18 km/hr.
To determine the velocity of the boat with respect to the river bank, we can use vector addition.
Step 1: Draw a diagram
Draw a diagram representing the river and the boat's motion. Place the boat's velocity vector northwards and the river's velocity vector eastwards.
Step 2: Decompose the vectors
Break down the boat's velocity into its components: a north component (Vb,n) and an east component (Vb,e). Similarly, break down the river's velocity into its components: a north component (Vr,n) and an east component (Vr,e).
Given:
Boat's velocity: 10 km/hr due north
River's velocity: 5 km/hr due east
So, we have:
Vb,n = 10 km/hr
Vr,e = 5 km/hr
Step 3: Add the components
To find the resulting velocity of the boat with respect to the river bank, add the corresponding components together.
Vb,on the river bank = Vb,n + Vr,e
Substituting the given values:
Vb,on the river bank = 10 km/hr + 5 km/hr
Step 4: Calculate the final velocity
Perform the addition to find the final velocity of the boat with respect to the river bank.
Vb,on the river bank = 15 km/hr
Therefore, the velocity of the boat with respect to the river bank is 15 km/hr.
Draw the velocity vectors.
The boat's speed s = √(10^2+5^2)
The boat's angle relative to the direct crossing line is NθE where tanθ = 5/10
Now, what is θ relative to the bank?