How do I draw the following problem so I have something to refer to when answering a) and b)?
A river is 2 km wide and flows at 6 km/h. A motor boat that has a speed of
20 km/h in still water heads out from one bank perpendicular to the current.
A marina lies directly across the river on the opposite bank.
a. How far downstream from the marina will the boat reach the other bank? (0.6 km)
b. How long will it take? (6 min)
Although the boat is pointed directly across, it does not travel perpendicular to shore. This is because, relative to the land, there is a Vx = 6 km/h component along the stream direction due to the river flow. There is also a Vy component of 20 km/h across the stream. The crossing time is 2.0 km/20 km/h = 0.1 h (6 minutes). The distance the boat drifts downstream in that time is 6 km/h*0.1h = 0.6 km
To draw the problem, you can create a simple diagram that represents the scenario described. Here are the steps to draw the diagram:
1. Start with a straight line to represent the width of the river. Label it as "2 km."
2. Draw a small arrow perpendicular to the river, which represents the motor boat heading out from one bank. Label it with an "M" to represent the motor boat.
3. Mark a point on the opposite bank, representing the marina. Label it as "Marina."
4. Indicate the direction of the river's flow by drawing an arrow parallel to the width of the river. Label it with "6 km/h" to represent the speed of the river's current.
5. Add a dotted line that starts at the boat and reaches the other bank at a certain distance. Label this distance as "x km," representing the distance downstream from the marina where the boat reaches the other bank.
Your diagram should now include a river with its width labeled, a motor boat departing from one bank, a marina on the opposite bank, the direction of the river's flow, and a dotted line representing the distance downstream from the marina.
Now, using this diagram, you can refer to it to answer parts a) and b) of the problem.
a. From the diagram, you can see that the boat needs to travel the width of the river plus the distance downstream to reach the other bank. Therefore, the distance downstream from the marina where the boat will reach the other bank is the sum of the width of the river and the previously unknown distance x. In this case, that distance is 2 km + x km = 2 + x km. Given in the problem statement that the boat will reach a distance of 0.6 km downstream, the answer to part a) is 0.6 km.
b. To determine how long it will take for the boat to reach the other bank, you can use the formula: time = distance/speed. The distance the boat needs to travel includes the width of the river (2 km) and the distance downstream (0.6 km). Therefore, the total distance is 2 km + 0.6 km = 2.6 km. The boat's speed in still water is given as 20 km/h. Plugging in these values into the formula, the time it takes for the boat to reach the other bank is 2.6 km / 20 km/h = 0.13 hours. To convert this time to minutes, multiply by 60: 0.13 hours * 60 min/hour = 7.8 min. Rounded to the nearest whole number, the answer to part b) is 8 minutes.
Using the drawn diagram and the explanations above, you can easily refer to it when answering parts a) and b) of the problem.