Projectile Motion #3: Cross River in 47s at 3.64 m/s

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Homework Help Overview

The discussion revolves around a projectile motion problem involving a boat crossing a river with a current. The boat's speed in still water and the river's width are provided, along with the current's speed. Participants are exploring the implications of these factors on the boat's trajectory and timing.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to determine the downstream distance the boat travels while crossing the river and are questioning how to set up the calculations for this part of the problem. There is discussion about the boat's speed relative to the shore and the effects of the current.

Discussion Status

Some participants have provided insights into the boat's movement across the river and downstream, while others are seeking clarification on how to calculate the downstream distance. There is an ongoing exploration of the relationship between the boat's speed across the river and the current's influence.

Contextual Notes

Participants are working within the constraints of the problem, including the boat's speed in still water, the river's width, and the current's speed. There is a specific focus on the setup for calculating the downstream distance, which remains unresolved.

Kildars
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A boat can travel at a speed of 3.4 m/s in still water. A river that is 160 m wide has a current that flows 1.3 m/s due West.

a) If the boat points its bow directly across the river, how fast does the boat travel relative to the shore?
3.64 m/s
b) How long will it take to cross the river?
47.0588 s
c) Fow far downriver will it land (the distance on the bank from the point directly across from the starting point to the landing point)?
m
d) At what angle should the boat be pointed in order to arrive at a point directly across from the starting point? Assume North is directly across the river.
° E of N
e) How long does that take?
s

I got A and B but I don't know how to setup C -- Any ideas?
 
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How fast is the boat going downstream? How far does it get in the time it takes to cross the river?
 
He's moving 3.4 + 1.3 so 4.5 m/s downstream and it would take him 47.0588 s to get across according to B.
 
Doc?! You there?
 
Kildars said:
He's moving 3.4 + 1.3 so 4.5 m/s downstream
No, he's moving 3.4 m/s across and 1.3 m/s downstream. (He points the boat directly across, which gets him across in the quickest time possible but requires him to move downstream along with the current. If he wants to go straight across the river without being dragged by the current, he'll have to point the boat at an angle--that's part d.)
and it would take him 47.0588 s to get across according to B.
Right, so how far does he get downstream in that time?
 

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