the downstream problem is perpendicular to and therefore independent of (except in time) the across problem
400 = 10 t
t = 40 seconds
then
d = 2 t = 80 m
400 = 10 t
t = 40 seconds
then
d = 2 t = 80 m
(a) Speed of the boat with respect to the water = 10 m/s
Speed of the river = 2.0 m/s
Since the boat is moving perpendicular to the river, the effective velocity of the boat (resultant velocity) will be the vector sum of the boat's velocity with respect to the water and the river's velocity.
Using the Pythagorean theorem, we can find the effective velocity of the boat:
Effective velocity = √((velocity of boat)^2 + (velocity of river)^2)
= √((10 m/s)^2 + (2 m/s)^2)
= √(100 m^2/s^2 + 4 m^2/s^2)
= √(104 m^2/s^2)
≈ 10.2 m/s
Now, we can find the time taken by the boat to cross the river using the formula:
Time = Distance / Speed
Distance to cross the river = width of the river = 400 m
Speed of the boat with respect to the water = 10 m/s
Time taken by the boat to cross the river = Distance / Speed
= 400 m / 10.2 m/s
≈ 39.2 s
Therefore, the time taken by the boat to reach the opposite bank is approximately 39.2 seconds.
(b) To find how far from the point directly opposite to the starting point the boat reaches the opposite bank, we can use the formula:
Distance = Speed x Time
Speed of the river = 2.0 m/s
Time taken by the boat to cross the river = 39.2 s
Distance from the point directly opposite to the starting point to the opposite bank = Speed of the river x Time
= 2.0 m/s x 39.2 s
≈ 78.4 m
Therefore, the boat reaches a distance of approximately 78.4 meters from the point directly opposite to the starting point when it reaches the opposite bank.