A person who can swim at 3 m/s wishes to swim straight across a river flowing at 2 m/s south. What heading should they swim at? How long will it take to cross the river if it is 56 m wide?
If an airplane wishes to fly north east at 300 mph has a wind blowing from 300 degrees at 60 mph, what heading and velocity must they have to accomplish this?
thats another question that i have
To determine the heading the person should swim at, we need to consider the relative velocities of the swimmer and the river. Since the swimmer can swim at a constant speed of 3 m/s and the river is flowing at a constant speed of 2 m/s south, the swimmer needs to swim at a heading that counteracts the velocity of the river and ensures a straight path across.
First, let's break down the velocities into their north (up) and south (down) components. The swimmer's velocity can be considered as 3 m/s north (up) and the river's velocity as 2 m/s south (down). Since they are perpendicular to each other, we can use vector addition to find the resultant velocity.
Subtracting the southward velocity of the river from the northward velocity of the swimmer, we get:
Resultant velocity = 3 m/s north - 2 m/s south.
Simplifying the expression gives us:
Resultant velocity = 3 m/s + 2 m/s = 5 m/s.
So, to counteract the river's flow and maintain a straight path across, the person should swim straight north with a heading of 0 degrees (or straight up).
To calculate the time it will take to cross the river, we can use the formula:
Time = Distance / Speed.
In this case, the distance is given as 56 m, and the speed of the swimmer across the river is still 3 m/s. Since the person is swimming straight across the river, their speed remains unchanged.
Plugging in the values, we have:
Time = 56 m / 3 m/s.
Calculating this gives us:
Time ≈ 18.67 seconds.
Therefore, it will take approximately 18.67 seconds to cross the 56-meter wide river.