A man is rowing a boat at 9km/h in the river 1.5km wide in which current is 5km/h.in which direction should he head in order to get across the river in the shortest possible time? how much time will it take?
a. Vb - 5i = 9.
Vb = 9 + 5i = 10.3km/h[29.1o] N. of E. = Velocity of boat.
b. d = V*t = 1.5.
9 * t = 1.5,
t = 0.166h = 10 min.
he wants to cross straight over, so he needs to head upstream at an angle x, where
sinx = 5/9
That makes his speed across 7.48 km/hr
So, how long will it take to cover the 1.5 km?
To determine the direction in which the man should head in order to get across the river in the shortest possible time, we need to consider the velocity vectors of the boat and the river current.
The velocity vector of the boat is 9 km/h in the direction the man rows, and the velocity vector of the river current is 5 km/h perpendicular to the direction the man rows.
To find the total velocity of the boat relative to the ground, we need to combine the velocity vectors of the boat and the river current. This can be achieved by using vector addition.
We can create a right triangle with the width of the river (1.5 km) as the base and the speed of the river current (5 km/h) as the height. The resulting hypotenuse represents the ground speed of the boat.
Using the Pythagorean theorem, we can calculate the ground speed of the boat as follows:
Ground Speed = √(Boat Speed^2 + Current Speed^2)
= √(9^2 + 5^2)
= √(81 + 25)
= √106
≈ 10.3 km/h
The man should attempt to row the boat in the direction opposite to the direction of the river current, as this will cancel out the effect of the current as much as possible and minimize the ground speed required to cross the river.
Now, we can calculate the time it will take for the boat to cross the 1.5 km width of the river. We already know the ground speed of the boat is approximately 10.3 km/h.
Time = Distance / Speed
= 1.5 km / 10.3 km/h
≈ 0.15 hours
To convert the time to minutes, we can multiply by 60:
0.15 hours * 60 minutes/hour = 9 minutes
Therefore, the man should row the boat opposite to the direction of the river current and it will take approximately 9 minutes to cross the river.