Solve a Simple Physics Problem: Boat Speed and River Flow in 30 Minutes

[BuBbLeS01]

Homework Statement

A boat can move at 30 km/hr in still water. how long will it take to move 12 km upstream in a river flowing 6.0 km/hr.

I know the answer is 30 min but the way my teacher explained it is very difficult to remember can someone show me another way to do this problem?

the way she showed us:
Vbg = 30 km/hr
Vbr = Vbg + Vgr = 24 km/hr = 0.4 km/min
Vrg = 6.0 km/hr
Vgr = -6.0 km/hr + 12/0.4 = 30 min

 

[learningphysics]

Do you agree that adding the velocity of the boat relative to the water + velocity of the water = velocity of the boat relative to ground (ie: net velocity) ?

 

[m2003]

There are a few different ways to solve this problem, so I will provide a few options for you to consider.

1. The first method is similar to the one your teacher showed you. We know that the boat's speed in still water is 30 km/hr, and we also know that the river's flow is 6.0 km/hr. When the boat is moving upstream, it is going against the direction of the river's flow, so we need to subtract the river's flow from the boat's speed. This gives us a net speed of 30 km/hr - 6.0 km/hr = 24 km/hr. We can then use the formula distance = speed x time to solve for time. In this case, we want to find the time it takes to travel 12 km, so we have 12 km = 24 km/hr x time. Solving for time, we get 12 km / 24 km/hr = 0.5 hr. Since we want the answer in minutes, we can convert 0.5 hr to minutes by multiplying by 60, giving us a final answer of 30 minutes.

2. Another way to solve this problem is to use the concept of relative velocities. In this method, we consider the boat and the river as two separate systems, and we calculate the relative velocity between them. When the boat is moving upstream, it is actually moving slower than its speed in still water because it is also moving in the opposite direction of the river's flow. So, the relative velocity between the boat and the river is 30 km/hr - 6.0 km/hr = 24 km/hr. We can then use the formula distance = relative velocity x time to solve for time. In this case, we want to find the time it takes to travel 12 km, so we have 12 km = 24 km/hr x time. Solving for time, we get 12 km / 24 km/hr = 0.5 hr. Again, we can convert 0.5 hr to minutes by multiplying by 60, giving us a final answer of 30 minutes.

3. Finally, we can also solve this problem using the concept of vectors. In this method, we consider the boat's velocity as a vector with a magnitude of 30 km/hr and a direction opposite to the river's flow. We can then break down this velocity into its horizontal and vertical components