A boat travelling at 30km/hr relative to water is headed away from the bank of a river and downstream. The river is 1/2 km wide and flows at 6km/hr. The boat arrives at the opposite bank in 1.24 min.
I calculated the perpendicular component of the boat relative to the water as 24km/hr.
I calculated the total downstream component of the boats motion as 24 km/hr (with the parallel component of the velocity of the boat relative to the water at 18km/hr).
And I calculated the direction in which the boat moves relative to land which is 45degrees to the bank.
I need help with calculating the distance the boat moves downstream as it crosses the river.
I get (0.5/1.24)*60 = 24.2 km/hr for the perpendicular component. Don't do any rounding off yet.
Parallel component of velocity, relative to water = sqrt[(30^2 - (24.2)^2] = 17.7 km/h
The parallel (downstream) velocity of the boat relative to land is 17.7 + 6 = 23.7 km/hr
The distance it drifts downstream in 1.24 minutes *(23.7 km/h)*(1h/60 min)
= 0.49 km
This agrees well with your 45 degree boat direction relative to land . The downstream drift nearly equals the river's width
thank you for the help!
To calculate the distance the boat moves downstream as it crosses the river, we can use the concept of relative velocity.
Let's break down the boat's motion into two components: the velocity of the boat relative to the water and the velocity of the water itself.
The boat's velocity relative to the water is given as 30 km/hr, and the velocity of the river flow is given as 6 km/hr.
To determine the resultant velocity of the boat as it moves downstream, we can use vector addition. The resultant velocity will be the sum of the boat's velocity relative to the water and the velocity of the water.
The perpendicular component of the boat's velocity relative to the water, which gives us the speed of the boat downstream, is 24 km/hr. This is because we have already calculated the perpendicular component by finding the square root of the sum of the squares of the boat's velocity relative to the water and the velocity of the water, using the Pythagorean theorem.
Now we can use the formula distance = speed × time to find the distance the boat moves downstream. The speed of the boat downstream is 24 km/hr, and the time taken to cross the river is given as 1.24 minutes.
However, we need to convert the time to hours to match the units of speed. There are 60 minutes in an hour, so 1.24 minutes is equal to 1.24/60 hours, which is approximately 0.0207 hours.
Now we can calculate the distance as follows:
Distance = Speed × Time
Distance = 24 km/hr × 0.0207 hours
Distance ≈ 0.4968 km
Therefore, the boat moves approximately 0.4968 km downstream as it crosses the river.