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Using the conditions of the foregoing problem, draw the approximate time dependence of moduli of the normal w_n and tangent w_tau acceleration vectors, as well as of the projection of the total acceleration vector w_v on the velocity vector direction. |
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Answer» As `vecvuarr uarr hatu_t` all the moments of TIME. THUS `nu^2=nu_t^2-2g tnu_0sin alpha+g^2t^2` Now, `w_t=(dnu_t)/(dt)=(1)/(2v_t)(d)/(dt)(v_t^2)=1/v_t(g^2t-gv_0sin alpha)` `=-g/v_t(v_0sin alpha-g t)=-"g" (v_y)/(v_t)` Hence `|w_t|="g"(|v_y|)/(v)` Now `w_n=SQRT(w^2-w_t^2)=sqrt(g^2-"g"^2(v_y^2)/(v_t^2))` or `w_n="g"(v_x)/(v_t)` (where `v_x=sqrt(v_t^2-v_y^2)` As `vecvuarr uarr hatv_t` during time of motion `w_v=w_t=-"g" (v_y)/(v)` On the basis of obtained expressions or facts the sought PLOTS can be drawn as shown in the figure of answer sheet. |
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