Relative Velocity: Al & Bob's Trip to Ted's Place

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SUMMARY

In the discussion about Al and Bob's trip to Ted's place, it is established that Al must wait 14.62 seconds after Bob sets out to ensure they arrive simultaneously. Al swims directly across the river, taking 142.85 seconds to reach Ted, while Bob, who swims at an angle to account for the river's current, takes 128.20 seconds. The calculations involve determining the angles of their respective swimming paths and the effective velocities due to the river's flow. The discussion highlights the importance of vector addition in calculating the most direct route for Bob.

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  • Ability to calculate time, distance, and speed using the formula t = D/V
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pinkyjoshi65
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Two swimmers, Al and Bob, live on opposite shores of a 200.0 m wide river that flows east at 0.70 m/s. Al lives on the north shore and Bob lives on the south shore. They both set out to visit a mutual friend, Ted, who lives on the north shore at a point 100.0 m upstream from Al and 100.0 m downstream from Bob. Both swimmers can swim at 1.4 m/s through the water. How much time must Al wait after Bob sets out so that they both arrive at Ted's place at the same time? Both swimmers make their trips by the most direct routes.

So, first I can find the time taken by Al.
t=D/V_ag
= 100/V_aw-V_wg
=100/0.7= 142.85 Seconds

Now, for Bob

we could use trig to find the angle (beta) of his most direct route.
but 1st we need to find theta.

So using tri==== Tan(theta)= 200/100
And we get theta as 63.4 degrees.
Then we can find beta, since one angle is 90 and the other is 63.4.
so beta will be= 26.5 degrees
Then, Sin(26.5)= 0.7/hypotunese
hence hypotunese= 1.56m/s
This is bob's speed (most direct route)
Now for his time, t= 200/1.56= 128.20 seconds.

T1-T2= 142.82-128.20= 14.62 seconds.
hence Al must wait for 14.62 seconds after Bob has left inorder for both of them to reach Ted's place at the same time.

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Your answer for Al is correct but you need to show that he can reach the other bank in that time, too.

Regards Bob, the angle his most direct route makes with the banks is your theta and the angle it makes perpendicular to the banks is your beta (you miscalculate beta by 0.01 degrees).

Bob's "most direct route" diagram can't be used as the vector addition triangle to find the velocity that he travels on that route. Imagine yourself as Bob, swimming. What direction would you have point your body so that addding your swimming velocity to the river's flow velocity, you travel on the most direct route?
 
I guess, Bob will have to travel towards the north direction, and then let the eastwards water current carry him.