(d) Supposing that , find the duration of the motion . · OlympiadBench #957

Physics · mechanics

Problem

(d) Supposing that β<<gv0\beta<<\frac{g}{v_{0}}, find the duration of the motion TT. Given constants: 2. Trajectory of a point mass A point mass on the ground is thrown with initial velocity v⃗0\vec{v}_{0} that makes an angle θ\theta with the horizontal. Assuming that air friction is negligible, Context question: (a) What value of θ\theta maximizes the range? Context answer: π4\frac{\pi}{4} Context question: (b) What value of θ\theta maximizes the surface area under the trajectory curve? Context answer: π/3\pi / 3 Context question: (c) What is the answer for (a), if the point mass is thrown from an apartment of height hh ? Now assume that we have a frictional force that is proportional to the velocity vector, such that the equation of motion is as follows dv⃗dt=g⃗−βv⃗\frac{d \vec{v}}{d t}=\vec{g}-\beta \vec{v} Context answer: arcsin⁡(12v0v02+gh)\arcsin \left(\frac{1}{\sqrt{2}} \frac{v_{0}}{\sqrt{v_{0}^{2}+g h}}\right)

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