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

[bobpeg123]

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:
D_T (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

 

[diazona]

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:
D_T (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.

 

[bobpeg123]

But does that mean that the mass isn't important, or that gravity therefore doesn't matter?

 

[diazona]

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.

 

[bobpeg123]

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.