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songoku
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Homework Statement
A particle of mass m kg is projected under gravity with horizontal and vertical components of velocity U and V. There is horizontal resistance of magnitude mku, where k is constant and u is horizontal component of the velocity at t seconds. No vertical resistance present.
(i) Show horizontal range from point of projection is [itex]R = \frac{U}{k} (1 - e^{-kT})[/itex] where T = 2V/g
(ii) Find the horizontal distance D traveled before reaching the highest point of its path
(iii) Show that D > R/2
Homework Equations
Integration
Newton's law
Kinematics
The Attempt at a Solution
(i) I did this and got the answer
(ii) For this question, is it only changing the time from T to T/2? So the answer is [itex]R = \frac{U}{k} (1 - e^{-\frac{kT}{2}})[/itex] ?
(iii) I do not know how to do this one.
[itex]\frac{D}{R} = \frac{1 - e^{-\frac{kT}{2}}}{1 - e^{-kT}}[/itex] and I need to show this will be bigger than 1/2
Thanks