Explanation:
Mass of Apple, [tex]m_a=0.125\ kg[/tex]
Mass of orange, [tex]m_o=0.16\ kg[/tex]
Initial speed of orange, [tex]u_o=1.18i[/tex]
Initial speed of Apple, [tex]u_a=-1.13i[/tex]
Final speed of the orange, [tex]v_o=-0.999j[/tex]
(a) Let [tex]v_a[/tex] is the final sped of the apple. It can be calculated using the law of conservation of momentum as :
[tex]m_au_a+m_ou_o=m_av_a+m_ov_o[/tex]
[tex]m_av_a=(m_au_a+m_ou_o)-m_ov_o[/tex]
[tex]m_av_a=(0.125\times (-1.13i)+0.16\times (1.18i))-0.16\times (-0.999j)[/tex]
[tex]m_av_a=(-0.141i+0.1888i)+0.159j[/tex]
[tex]m_av_a=0.0478i+0.159j[/tex]
[tex]v_a=\dfrac{0.0478i+0.159j}{0.125}[/tex]
[tex]v_a=0.382i+1.27j[/tex]
[tex]|v_a|=\sqrt{0.382^2+1.27^2}=1.32\ m/s[/tex]
So, the final speed of the apple is 1.32 m/s
(b) The direction of the apple in this case is given by:
[tex]tan\theta=\dfrac{1.27}{0.382}[/tex]
[tex]\theta=73.25^{\circ}[/tex]
Hence, this is the required solution.
