- #1
Georgepowell
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I have done M1, M2, C1 C2 C3 & C4 (A level maths modules, M meaning mechanics and C meaning core/pure). In M2 we learned how to predict how a particle moves under gravity when projected at an angle, and we always ignored air resistance. In C4 we have learned how to integrate a whole range of functions. This is not homework or school work
I wondered how to predict the movement of a particle if the air resistance WAS taken into account. So I tried to figure it out and I just need to know if I have done it right. Here is the [very simple] example:
A particle of mass one kg is initially traveling at 10m/s, air resistance is equal to a tenth of its current velocity. Find its velocity in terms of time.
I wrote:
F = ma
v/10 = a
a = v/10
acceleration is also dv/dt so:
dv/dt = v/10
1/v dv = 1/10 dt
integrate both sides you get:
ln(v) = t/10 + lnA
v = Ae^(t/10)
t = 0, v = 10
10 = Ae^0
so final answer is:
v = 10e^(t/10)
is this right? is there another way to do it?
I wondered how to predict the movement of a particle if the air resistance WAS taken into account. So I tried to figure it out and I just need to know if I have done it right. Here is the [very simple] example:
A particle of mass one kg is initially traveling at 10m/s, air resistance is equal to a tenth of its current velocity. Find its velocity in terms of time.
I wrote:
F = ma
v/10 = a
a = v/10
acceleration is also dv/dt so:
dv/dt = v/10
1/v dv = 1/10 dt
integrate both sides you get:
ln(v) = t/10 + lnA
v = Ae^(t/10)
t = 0, v = 10
10 = Ae^0
so final answer is:
v = 10e^(t/10)
is this right? is there another way to do it?