Question 1 P1 = 5.4 kg m/s. 32.9° south of up P2 = 13.9 kg m/s, 33.4° south of down Pi +P2 = [Select ] kg m/s. I Select] [ Select] [ Select ] (relative to up/down)

As per the guide lines first question is solved, kindly post other question as new post.

Question 1

Consider south as $\hat{i}$ direction, up as $\hat{j}$ and down as $-\hat{j}$ direction.

South of up means the vector is in south - up plane, the angle is measured from up towards south.

South of down means the vector is in south - down plane, the angle is measured from down towards south.

$$\begin{gathered} {\overrightarrow{p}}_1=\left(5.4 \mathrm{kg}\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.\right) 32.9° \mathrm{south} \mathrm{of} \mathrm{up} \\ =\left(5.4 \mathrm{kg}\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.\right)\left[\sin 32.9° \hat{\mathrm{i}}+\cos 32.9° \hat{\mathrm{j}}\right] \\ =\left(2.93314203 \hat{\mathrm{i}} +4.533947268 \hat{\mathrm{j}}\right) \mathrm{kg}\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right. \\ {\overrightarrow{\mathrm{p}}}_2=\left(13.9 \mathrm{kg}\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.\right) 33.4° \mathrm{south} \mathrm{of} \mathrm{down} \\ =\left(13.9 \mathrm{kg}\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.\right)\left[\sin 33.4° \hat{\mathrm{i}}-\cos 33.4° \hat{\mathrm{j}}\right] \\ =\left(7.651682287 \hat{\mathrm{i}}-11.6043853 \hat{\mathrm{j}}\right) \mathrm{kg}\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right. \end{gathered}$$