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.

Answer

`(##IROD_V01_C01_E01_030_S01##)`

Explanation

We have, `v_x=v_0cosalpha`, `v_y=v_0sin alpha-g t`
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.