Adam can swin at a rate of 2km/h in still water. At what angle to the bank of a river must he head if he wants to swim directly across the rivver and the current in the river moves at the rate of 1 km/h?
To determine the angle at which Adam must head relative to the bank, we need to consider the effect of the current on his swimming path. Here's how we can approach this:
Step 1: Draw a diagram to represent the situation. The river can be represented by a straight line, and Adam's motion can be shown as a vector pointing across the river. Label the speed of Adam in still water as 2 km/h and the speed of the river current as 1 km/h.
Step 2: Split Adam's velocity into two components: one parallel to the bank and one perpendicular to the bank. The component parallel to the bank represents Adam's swimming speed, while the component perpendicular to the bank represents the effect of the current. Since the current is flowing perpendicular to the bank, we can consider the component perpendicular to the bank as the same as the speed of the current itself.
Step 3: Use trigonometry to find the angle. We can use the tangent function to determine the angle at which Adam should swim. The equation for the tangent of an angle is given by the ratio of the side opposite the angle to the side adjacent to the angle.
In this case, the side opposite the angle is the speed of the current (1 km/h), and the side adjacent to the angle is Adam's swimming speed in still water (2 km/h). Therefore, the tangent of the angle is 1/2 or 0.5.
Step 4: Calculate the angle. You can use the inverse tangent function, denoted as atan, to find the angle. In this case, atan(0.5) will give you the result in radians. To convert the result to degrees, multiply it by 180/π (approximately 57.3).
Using a calculator or programming language that supports trigonometric functions, evaluate atan(0.5) and multiply the result by 180/π to find the angle in degrees.
Alternatively, you can use the arctan function on a scientific calculator or search online for an angle calculator and enter the value 0.5 to obtain the angle directly.
By following these steps, you will find that Adam should head at an angle of approximately 26.6 degrees to the bank in order to swim directly across the river and counteract the effect of the current.