If a kayak can travel straight across a 50m wide river and can paddle at 8 m/s and the river flow has a current of 5 m/s west what is the maximum velocity in km/h (don't forget the direction) with the help of the current? And if the current is frustrating what is the slowest velocity possible in km/h (don't forget the direction)
To find the maximum velocity with the help of the current, we need to add the velocities of the kayak and the river flow. Since both velocities are in different directions, we need to take into account their signs.
1. Convert the kayak's paddling velocity from m/s to km/h:
Since 1 km = 1000 m and 1 hour = 3600 seconds, we can convert m/s to km/h by multiplying the value by 3.6. Therefore, the kayak's paddling velocity is 8 m/s * 3.6 = 28.8 km/h.
2. Convert the river flow velocity from m/s to km/h:
Using the same conversion, the river's flow velocity is 5 m/s * 3.6 = 18 km/h.
3. Determine the maximum velocity by adding the velocities of the kayak and the river flow:
In this case, since the river flow is in the opposite direction to the kayak's movement, we subtract its velocity. Therefore, the maximum velocity is 28.8 km/h - 18 km/h = 10.8 km/h westward.
To find the slowest possible velocity when the current is frustrating, we need to subtract the river flow velocity from the kayak's paddling velocity.
4. Determine the slowest velocity by subtracting the river flow velocity from the kayak's velocity:
Since the river flow is frustrating and acts as a resistance, we subtract the velocity of the river flow from the kayak's velocity. Therefore, the slowest velocity is 28.8 km/h - 18 km/h = 10.8 km/h eastward.
So, the maximum velocity with the help of the current is 10.8 km/h westward, and the slowest velocity when the current is frustrating is 10.8 km/h eastward.