Use the given equation for magnitude of drag force to calculate time taken

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Homework Help Overview

The discussion revolves around a physics problem involving a ball of mass 0.5 kg traveling horizontally through the air, experiencing a drag force defined by the equation DT(t) = 0.01[v(t)]². The problem states that the ball's speed decreases from 10 m/s to 8 m/s over a time interval t, and participants are tasked with calculating this time interval.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants express uncertainty about how to apply the drag force equation in a horizontal context, questioning the relevance of gravity and mass in this scenario. Some participants attempt calculations based on the drag force equation but express doubt about the reasonableness of their results.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions related to drag force in horizontal motion. Some guidance has been offered regarding the independence of drag force from gravitational effects, but no consensus has been reached on the calculations or the approach to finding time t.

Contextual Notes

Participants are grappling with the application of drag force equations typically used for vertical motion to a horizontal scenario, leading to questions about the role of mass and gravity in this context. There is also a noted confusion regarding the implications of changing velocity on drag force during the time interval.

bobpeg123
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Homework Statement



A ball of mass 0.5 kg traveling horizontally through the air with speed v(t) experiences
a drag force DT (t) whose magnitude is given by:
DT (t ) = 0.01[v (t )] 2
The speed of the ball is found to reduce from 10 m/s to 8 m/s over a time interval t,
during which time the ball continues to travel horizontally. Calculate t.


Homework Equations


I'm not entirely sure where to start with this. My notes give me the equation for drag forces falling vertically but I wasn't sure what to do because it's traveling horizontally.


The Attempt at a Solution


 
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bobpeg123 said:

Homework Statement



A ball of mass 0.5 kg traveling horizontally through the air with speed v(t) experiences
a drag force DT (t) whose magnitude is given by:
DT (t ) = 0.01[v (t )] 2
The speed of the ball is found to reduce from 10 m/s to 8 m/s over a time interval t,
during which time the ball continues to travel horizontally. Calculate t.


Homework Equations


I'm not entirely sure where to start with this. My notes give me the equation for drag forces falling vertically but I wasn't sure what to do because it's traveling horizontally.
Why would it be different for something moving horizontally?

Remember, the drag force always points in the opposite direction of the velocity.
 
But does that mean that the mass isn't important, or that gravity therefore doesn't matter?
 
Not for drag force. For a given object in a given fluid (air), the drag force is completely determined by only two things: how fast the object is moving (drag force is proportional to velocity squared) and which way it's moving (drag force always opposes the velocity). It doesn't matter whether gravity is in effect or not.
 
Ok, so I tried again and I got,

for v = 100m/s, D = 10N,

using D = bv^2, b=10/100^2 = 0.001

and then using v(t) = {sqrt(mg/b)... expotential stuff, which gave me an answer of 23m/s after 3 secs, but I don't know if that seems reasonable because as the velocity drops, so does the drag so how would it drop 77m/s in 3 seconds.
 

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