A man wishes to cross a river from A to B, a distance of 800m. He can row at 8km per hour, in what direction should he head the boat to travel directly from A to B? How long does it take him to reach B?
Please show working. Thank You!
There is no current specified so row straight across :)
To determine the direction in which the man should head the boat to travel directly from A to B, we need to consider the effect of the river's current. If there is a current in the river, it will push the boat off course, and the man should adjust his heading to counteract this.
Let's assume that the river's current is flowing directly from north to south, perpendicular to the direction from A to B.
To find the correct direction, the man should point the boat slightly upstream, in the direction opposite to the current. This is because the current will push the boat downstream, but by pointing the boat upstream, the resulting drift will be canceled out, allowing the boat to travel directly across from A to B.
Next, let's determine the time it takes the man to reach point B.
We know that the man can row at a speed of 8 km/h. To convert this to meters per second, we divide 8 by 3.6 (since 1 km = 1000 m and 1 hour = 3600 seconds). Therefore, the rowing speed is approximately 2.22 m/s.
To cover a distance of 800 meters at a speed of 2.22 m/s, we use the formula: time = distance / speed.
So, the time taken to reach B is 800 meters / 2.22 m/s = 360.36 seconds (rounded to two decimal places).
Therefore, it takes the man approximately 360.36 seconds to reach point B.
To summarize:
- The man should head the boat slightly upstream, in the direction opposite to the river's current.
- The time taken to reach point B is approximately 360.36 seconds.