A river flows due south with a speed of 2.00 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.20 m/s due east. The river is 800 m wide.
What is the magnitude of his velocity relative to the earth?
got it....4.65 m/s
What is the direction of his velocity relative to the earth?
got it....25.5 degrees south of east
How much time is required for the man to cross the river?
don't know...
How far south of his starting point will he reach the opposite bank?
don't know....
A river flows due south with a speed of 2.00 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.20 m/s due east. The river is 800 m wide.
What is the magnitude of his velocity relative to the earth?
got it....4.65 m/s correct
What is the direction of his velocity relative to the earth?
got it....25.5 degrees south of east
correct
How much time is required for the man to cross the river?
don't know...
What is the distance across (given) and his speed due east (given)?
How far south of his starting point will he reach the opposite bank?
don't know....
You know the time it takes to get across (just done), and his speed downstream (2.00m/s).
North of east degrees is 28...
To find the time required for the man to cross the river, we need to determine the distance across the river and his speed due east.
Given:
- Speed of the river (downstream) = 2.00 m/s
- Velocity of the boat relative to the water (eastward) = 4.20 m/s
- Width of the river = 800 m
To find the distance across the river, we can use the formula:
Distance = Speed x Time
The speed of the boat relative to the water can be split into two components:
- Eastward component: 4.20 m/s
- Southward component due to the river's flow: 2.00 m/s
The southward component doesn't contribute to the distance across the river, but it affects the time taken to cross.
Since the boat is moving due east, the northward component of the velocity cancels out with the southward flow of the river. This means that the boat will remain at the same latitude (north or south) throughout its journey.
Let's calculate the time required to cross the river:
Time = Distance / Speed
Distance across the river can be calculated using the Pythagorean theorem:
Distance = sqrt((Width of the river)^2 + (Southward component)^2)
Distance = sqrt((800 m)^2 + (2.00 m/s x Time)^2)
To find the time required, we'll set Distance equal to 800 m:
800 m = sqrt((800 m)^2 + (2.00 m/s x Time)^2)
Solving this equation will give us the time required for the man to cross the river.
To find the time it takes for the man to cross the river, we can use the formula:
time = distance / speed.
The distance across the river is given as 800 m, and the man's speed due east is 4.20 m/s. Plugging in these values, we get:
time = 800 m / 4.20 m/s
Simplifying the calculation, we find:
time = 190.48 seconds (rounded to two decimal places).
Therefore, it will take approximately 190.48 seconds for the man to cross the river.
To find how far south of his starting point the man will reach the opposite bank, we can use the formula:
distance south = time x speed downstream.
We have already calculated the time as 190.48 seconds, and the speed downstream (the river's speed) is given as 2.00 m/s. Plugging in these values, we get:
distance south = 190.48 s x 2.00 m/s
Simplifying the calculation, we find:
distance south = 380.96 meters (rounded to two decimal places).
Therefore, the man will reach a point approximately 380.96 meters south of his starting point when he reaches the opposite bank.