Projectile with Air resistance problem

[ZenchiT]

Guys! I think I've got the answer, I'm just going to upload it now. PLEASE BE RIGHT!

 

[ZenchiT]

Part a) F=mg and F=kv

Therefore mg=kv and v=19.6 (terminal velocity)
k = mg/v
k = mg/19.6

Part b)

Equation of motion -> -mg-kv = ma
(Sub in k =mg/v)
-2mg = ma
a = -2g
dv/dt = -2g
v = -2gt

Or maybe instead of subbing in k=mg/v It should have been mg/19.6?

Voila! Surely that's correct right?!

 

[haruspex]

Part a) F=mg and F=kv

Therefore mg=kv and v=19.6 (terminal velocity)
k = mg/v
k = mg/19.6

Part b)

Equation of motion -> -mg-kv = ma
(Sub in k =mg/v)
-2mg = ma
a = -2g
dv/dt = -2g
v = -2gt

Or maybe instead of subbing in k=mg/v It should have been mg/19.6?

Voila! Surely that's correct right?!

For the value of k, as I mentioned, if you are going to put numbers representing dimensioned quantities in the answer then you also need units. You don't need units for m and g since symbolic variables encapsulate the physical quantity independently of units. So you just need the right units for the 1/19.6 factor. What would those be?
For part b), you have used the same symbol v for two different velocities, the terminal velocity and the initial velocity. So, yes, you should have substituted mg/19.6 (with units) for k.

 

[ZenchiT]

For the value of k, as I mentioned, if you are going to put numbers representing dimensioned quantities in the answer then you also need units. You don't need units for m and g since symbolic variables encapsulate the physical quantity independently of units. So you just need the right units for the 1/19.6 factor. What would those be?
For part b), you have used the same symbol v for two different velocities, the terminal velocity and the initial velocity. So, yes, you should have substituted mg/19.6 (with units) for k.

Would it have N as the units because it has the same dimensions as force?

 

[haruspex]

Would it have N as the units because it has the same dimensions as force?

The problem is the lack of units for the 19.6. What units should that have? So what units will the 1/19.6 have?

 

[ZenchiT]

The problem is the lack of units for the 19.6. What units should that have? So what units will the 1/19.6 have?

m/s^-1 as its terminal velocity?

Thank you for the amount of help you've given me!

 

[haruspex]

m/s^-1 as its terminal velocity?

Thank you for the amount of help you've given me!

m/s, or ms^-1 (but not m/s^-1) is right for the 19.6. So what should it be for 1/19.6?

 

[rude man]

Part a) F=mg and F=kv

Therefore mg=kv and v=19.6 (terminal velocity)
k = mg/v
k = mg/19.6

Part b)

Equation of motion -> -mg-kv = ma
(Sub in k =mg/v)
-2mg = ma
a = -2g
dv/dt = -2g
v = -2gt

Or maybe instead of subbing in k=mg/v It should have been mg/19.6?

Voila! Surely that's correct right?!

Well, surely that is incorrect! (sorry to rain on your parade). The initial velocity is given as +6 m/s and your formula says initial velocity = 0!
Your equation of motion is correct but you are not solving the ODE correctly. Hint: try separation of variables.