Recent content by LondonLady

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    Solving a Cart Losing Mass Problem

    No the initial mass M does not include the mass of the sand. Thankyou very much for your comments, I will have a thorough read of them now.
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    Solving a Cart Losing Mass Problem

    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...
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    Solving a Rocket Equation: Mass, Velocity & Height

    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}...
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    Solving a Rocket Equation: Mass, Velocity & Height

    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...
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    How do vectors relate to perpendicularity in circular motion?

    Ahh! It didnt even occur to me that it might have changed into a product! Thankyou so much!
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    How do vectors relate to perpendicularity in circular motion?

    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} =...
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    How do vectors relate to perpendicularity in circular motion?

    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...
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    How to Calculate Work Done with Vectors?

    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...
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    When should a coastguard cutter start out to intercept a ship?

    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...
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    When should a coastguard cutter start out to intercept a ship?

    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...
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    When should a coastguard cutter start out to intercept a ship?

    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...
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