Calculating Maximum River Crossing Distance with Initial Velocity of 30 m/s

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Homework Help Overview

The discussion revolves around calculating the maximum width of a river that can be crossed by a ball thrown with an initial velocity of 30 m/s. The problem involves analyzing projectile motion and the relationship between horizontal and vertical components of motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss splitting the initial velocity into horizontal and vertical components and using these to analyze the motion. Questions arise regarding the necessity of time in the calculations and the interpretation of the variables involved, particularly concerning the width of the river.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the relationship between time and distance in the context of projectile motion. Some guidance has been offered regarding the use of diagrams and the components of velocity, but there is still uncertainty among participants about the overall approach.

Contextual Notes

Participants express confusion about the diagrams and the need for both x and y components in their calculations. There is a mention of needing to solve for time to determine the distance across the river, but the specifics of the setup remain unclear to some.

stressedgirl
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Homework Statement


If you can hurl a ball so that its initial speed is 30 m/s, what is the widest river it can cross?

v1 = 30m/s

Homework Equations


I am not sure with only the one variable given.

The Attempt at a Solution


Start with a x and y component diagram?
 
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Yes split the inital velocity into vertical and horizontal components.

Now consider vertical motion, when the ball lands on the ground again, the displacement is zero. Use y=vyt_0.5gt2 to get the time for this motion.

Now horizontally the Range (how wide your river is) is given by R=vxt

that 't' in the equation for 'R' is the time for the motion above.
 
Umm.. I don't understand. How would the 't' answer the question? Wouldn't I need a 'd' since it's asking how wide the river could be?

edit: SOrry I don't really understand what I'm even supposed to draw in the diagrams of the components
 
stressedgirl said:
Umm.. I don't understand. How would the 't' answer the question? Wouldn't I need a 'd' since it's asking how wide the river could be?

edit: SOrry I don't really understand what I'm even supposed to draw in the diagrams of the components

Solving for the 't' would get the 'd'.

Draw the 30m/s at an angle θ and split it into vertical and horizontal components.
 
Can I get something step by step please? I drew the components but I don't get why I even have to have both an x and the y. I just have two sets of axes and a theta angle at 90degrees
 
stressedgirl said:
Can I get something step by step please? I drew the components but I don't get why I even have to have both an x and the y. I just have two sets of axes and a theta angle at 90degrees

You will see why you need it soon.

Did you get your components as

y: 30sinθ

x: 30 cosθ

These are your initial velocity components

Now consider vertical motion: y=vyt-0.5gt2

When the ball hits the other side of the river, y = 0. So solve for 't' and tell me what you get.
 

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