Hi I have this problem involving a cart which is losing sand
It says:
A cart with initial mass M and a load of sand \frac{1}{2}M loses sand at the rate k kg/s. The cart is pulled horizontally by a force F. Find the differential equation for the rate of change of the carts velocity in terms...
Thankyou very much for your help Tide, I was a bit unsure about that dM_f bit.
I continued on but have got a bit confused again!
I know that the time for the burn out is 200 from the first part, so I did this
\displaystyle{-Mg = M\frac{dv_R}{dt} + v_0k}
\displaystyle{\frac{v_0k}{M}...
Im having this problem with a rocket equation. Ill state the problem then show what I've done
Let M = mass of rocket and fuel
M_f = mass of fuel
M_0 = rockets total initial mass (including fuel)
(this is given as 10^5 kg)
V_R = rockets velocity
A 10^5 kg rocket has a total...
hmm... thankyou for your reply. I can't agree though. I got
\vec{r}(t) = r\cos (t^2)\vec{i} + r\sin (t^2)\vec{j}
\vec{v}(t) = -2tr\sin (t^2)\vec{i} + 2tr\cos (t^2)\vec{j}
\vec{a}(t) = -4t^2r\cos(t^2)\vec{i} - 4t^2r\sin(t^2)\vec{j}
Then if you find the dot product
\vec{a}.\vec{v} =...
Im a bit confused about a question on circular motion that I'm answering. Ill state the entire question and then say what I am confused about.
In class we discussed circular motion for the case
\displaystyle{\frac{d\theta}{dt} = \omega}
Now assume that the circle has radius r and that...
Hello again
I have another question!
Suppose a particles initial position is \vec{r_1} = 2\vec{i} + 5\vec{j} - \vec{k} metres and its acted upon by a force \vec{F} = \vec{i} + \vec{j} + \vec{k} Newtons. Its final position is \vec{r_2} = -4\vec{i} + 3\vec{j} + \vec{k}. Find the work done by...
Hello, thankyou for your reply :smile:
Ahhh!
I started with \displaystyle{x = D\frac{u\cos \theta - v}{u \sin \theta}}
and differentiated. I found that at the minimum of x
\displaystyle{\cos \theta = \frac{u}{v}}
which would mean (after drawing a triangle) that...
Hi, thankyou! :smile:
Em, well first i designated the value of the distance that v starts behind u to be 'x'
So then I broke the u vector into u\cos \theta i + u\sin \theta j.
At the time of intersection 't' the two ships will be in the same place so i evaluated the x - y displacement...
Hi, I have this question which I am having trouble with
A ship is steaming parallel to a straight coastline, distance D offshore, at speed v. A coastguard cutter, whose speed is u (u<v) seta out from port to intercept the ship. Show that the cutter must start out before the ship passes a...