Answer
given,
mass of jogger = 67 kg
speed in east direction = 2.3 m/s
mass of jogger 2 = 70 Kg
speed = 1.3 m/s in 61 ° north of east.
jogger one
[tex]P_1 = m_1 v_1 \hat{i}[/tex]
[tex]P_1 = 67 \times 2.3\hat{i}[/tex]
[tex]P_1 = 154.1 \hat{i}[/tex]
[tex]P_2 = m_2 v_2 \hat{i} +m_2 v_2 \hat{j} [/tex]
[tex]P_2 = 70\times v cos \theta \hat{i} +70\times v sin \theta \hat{j} [/tex]
[tex]P_2 = 70\times 1.3 cos 61^0 \hat{i} +70\times 1.3 sin 61^0\hat{j} [/tex]
[tex]P_2 = 44.12\hat{i} +79.59\hat{j} [/tex]
now
P = P₁ + P₂
[tex]P = 198.22 \hat{i} +79.59 \hat{j} [/tex]
magnitude
[tex]P = \sqrt{198.22^2 + 79.59^2}[/tex]
[tex]P =213.60 kg.m/s[/tex]
[tex]\theta = tan^{-1}\dfrac{79.59}{198.22}[/tex]
[tex]\theta = 21.87[/tex]
the angle is [tex]\theta = 21.87[/tex] north of east
