A swimmer tries to go straight across a river that is 500m wide. The swimmer can swim at 1.5m/s. There is a current of .05m/s downstream. Calculate
a) the actual velocity of the swimmer
b) how long it will tale to reach the far shore
c) how far donstream the swimmer will hit the opposite shore.
So far I'm using pythagorean theorem to find the hypotenuse; I'm doing the squre root of 500^2+.5^2 and that's givving me 500.00025, but I don't really think I'm doing this correctly; I'd really appreciate some help with this. :)
No, not correct.
1) his actual velocity sqrt(1.5^2+.05^2)
2)time=500/1.5
3) distancedownstream=.05*time in b.
oh okay, thank you.
Could you mind explainig how you got the velocity, please?
The velocity over the ground is a right triangle sum of the across velocity plus stream velocity.
oh ok, I see that now; thank you very much! :)
To solve this problem, you can use vector addition. The velocity of the swimmer can be broken down into two components: the horizontal component, which is the speed at which the swimmer is trying to cross the river, and the vertical component, which is the speed at which the swimmer is being carried downstream by the current.
a) To find the actual velocity of the swimmer, you can use the Pythagorean theorem. The horizontal component is 1.5 m/s, and the vertical component is 0.05 m/s. So, the actual velocity can be calculated as follows:
v_actual = sqrt((1.5^2) + (0.05^2)) = sqrt(2.2525) ≈ 1.50 m/s
Therefore, the actual velocity of the swimmer is approximately 1.50 m/s.
b) To find how long it will take to reach the far shore, you can divide the distance by the horizontal component of the velocity:
time = distance / velocity
distance = 500 m (width of the river)
velocity = 1.5 m/s (horizontal component of the velocity)
time = 500 m / 1.5 m/s ≈ 333.33 s
Therefore, it will take approximately 333.33 seconds, or about 5 minutes and 33 seconds, for the swimmer to reach the far shore.
c) To find how far downstream the swimmer will hit the opposite shore, you can multiply the vertical component of the velocity by the time taken:
distance_downstream = velocity_vertical * time
velocity_vertical = 0.05 m/s (vertical component of the velocity)
time = 333.33 s
distance_downstream = 0.05 m/s * 333.33 s ≈ 16.67 m
Therefore, the swimmer will hit the opposite shore approximately 16.67 meters downstream from the starting point.