A canoeist sets out straight across a 2-miles wide river padding x miles/hr. The average current of the river is 10 miles/hr. The canoeist lands at the point which is 1 mile away from the point on the opposite side of the river. Calculate the value of x?
He went 2 miles in one tenth of an hour. He is wicked fast.
will report IP to college IT team
30
To calculate the value of x, we need to apply the concept of vector addition. The movement of the canoe can be broken down into two components:
1. The first component is the canoeist's speed paddling straight across the river. This will be denoted as Vc.
2. The second component is the effect of the river current pushing the canoe downstream. This will be denoted as Vr.
Since we are given that the average current of the river is 10 miles/hr, we can say Vr = 10 miles/hr.
The vector representing the displacement across the river is given as 2 miles. Let's call this vector D. Similarly, the displacement along the current is given as 1 mile. Let's call this vector DC (Downstream Current).
Now, let's consider the triangle formed by D, DC, and the vector representing the canoeist's upstream speed, Vc. We can use the Pythagorean theorem to relate these vectors:
|D|^2 = |DC|^2 + |Vc|^2
Squaring both sides, we have:
(2 miles)^2 = (1 mile)^2 + x^2
4 miles^2 = 1 mile^2 + x^2
Simplifying, we have:
3 miles^2 = x^2
Taking the square root of both sides, we get:
sqrt(3 miles^2) = sqrt(x^2)
sqrt(3) miles = x
So, the value of x is approximately sqrt(3) miles per hour.