jumpingbean35
New member
- Joined
- Jan 25, 2012
- Messages
- 2
Here is a question I have tried repeatedly and have not gotten anywhere close to the answer:
A ball with mass of .15kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is a force due to air resistance of v/30.
a) find the maximum height above the ground that the ball reaches
My work:
F=ma
-ma=-mg-v/30 divide by negative mass
a=-g-v/(m30) a=dv/dt
dv/dt= -g-v/(m30)
this is a separable differential equation:
dv/dt-v/(30m)=-g
multiply by integration factor e^(t/30m)
by chain rule:
∫ (e^(t/30m)v)' =-g ∫ e^(t/30m)
v=-44.1+ce^(t/30m)
v(0)=20, so c=64.1
v=ds/dt
integrating v gives
s=-44.1t+288.5e^(-t/30m)
max height occurs at v(t)=0
v(t)=0 at t=1.68 seconds
plugging t into s, I get 124.3m.
However, the answer is supposed to be 45.7m?
Can anyone spot where I am going wrong? I am not really sure about any of it, and don't know where to start with a different solution.
b)Find the time that the ball hits the ground
--I haven't started this part because I can't get the first part, but would I need a different differential equation for this? I think the first part is only valid for the upwards direction?
Thanks!
A ball with mass of .15kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is a force due to air resistance of v/30.
a) find the maximum height above the ground that the ball reaches
My work:
F=ma
-ma=-mg-v/30 divide by negative mass
a=-g-v/(m30) a=dv/dt
dv/dt= -g-v/(m30)
this is a separable differential equation:
dv/dt-v/(30m)=-g
multiply by integration factor e^(t/30m)
by chain rule:
∫ (e^(t/30m)v)' =-g ∫ e^(t/30m)
v=-44.1+ce^(t/30m)
v(0)=20, so c=64.1
v=ds/dt
integrating v gives
s=-44.1t+288.5e^(-t/30m)
max height occurs at v(t)=0
v(t)=0 at t=1.68 seconds
plugging t into s, I get 124.3m.
However, the answer is supposed to be 45.7m?
Can anyone spot where I am going wrong? I am not really sure about any of it, and don't know where to start with a different solution.
b)Find the time that the ball hits the ground
--I haven't started this part because I can't get the first part, but would I need a different differential equation for this? I think the first part is only valid for the upwards direction?
Thanks!