A kayak is moving across a stream that is flowing downstream at a velocity of 4 km/hour. The kayak's velocity is 3 km/hour. What is the magnitude of the kayak's velocity relative to the river bank?
In this case you must use the Pyth. Theorem.
so: 3^2 + 4^2 = c^2
9+16=c^2
c^2=25
c=5m/s
the answer is correct, but I cannot ensure you that the way to do it is 100%ly correct
To find the magnitude of the kayak's velocity relative to the river bank, we can use the concept of vector addition.
Let's say the velocity of the kayak is represented by vector K, and the velocity of the river stream is represented by vector R.
The magnitude of the kayak's velocity relative to the river bank can be represented by the magnitude of the resultant vector when adding vector K and vector R.
Given the velocity of the kayak (3 km/h) and the velocity of the river stream (4 km/h), we can find the magnitude of the kayak's velocity relative to the river bank as follows:
Resultant magnitude = sqrt((kayak velocity)^2 + (river stream velocity)^2)
Resultant magnitude = sqrt((3 km/h)^2 + (4 km/h)^2)
Resultant magnitude = sqrt(9 km^2/h^2 + 16 km^2/h^2)
Resultant magnitude = sqrt(25 km^2/h^2)
Resultant magnitude = 5 km/h
Therefore, the magnitude of the kayak's velocity relative to the river bank is 5 km/h.
To find the magnitude of the kayak's velocity relative to the river bank, we need to calculate the resultant velocity vector by considering the velocities of the kayak and the stream.
The kayak's velocity is given as 3 km/hour, which we'll call velocity vector K.
The stream's velocity is given as 4 km/hour, which we'll call velocity vector S. Since the stream is flowing downstream, its velocity is in the same direction as the positive x-axis.
To find the resultant velocity vector R (relative to the river bank), we need to add the velocity vectors of the kayak and the stream. Since they are both in the horizontal direction, we can simply add their magnitudes:
Magnitude of K = 3 km/hour
Magnitude of S = 4 km/hour
Adding the magnitudes, we get:
Magnitude of R = Magnitude of K + Magnitude of S
= 3 km/hour + 4 km/hour
= 7 km/hour
Therefore, the magnitude of the kayak's velocity relative to the river bank is 7 km/hour.
The question should clarify that 3 km/h is the kayak velocity with respect to the water, which would be the velocity in still water, rowing at the same power level. It is NOT the actual velocity as seen from shore, whjich is higher, since the kayer is paddling downstream.
Vkl = Vkw + Vwl, where:
Vkl is the velocity of the kayak with respect to land;
Vkw is the velocity of the kayak with respect to the water;
Vwl is the velocity of the water with respect to the land (i.e, the stream velocity of + 4 km/h).
Solve for Vkl
4 + 3 = ___ ?