Answer :
To solve this problem we will apply the linear motion kinematic equations. Just as we will also find the relative speed of the body through the conservation of momentum. Our data is given as
[tex]M = 157kg[/tex]
[tex]m = 46kg[/tex]
[tex]v_1 = 1.48m/s[/tex]
PART A)
From the conservation of momentum,
[tex]\text{Momentum of Plank+girl}+\text{Mometum of girl} = 0[/tex]
[tex](M+m)v_2+mv_1 = 0[/tex]
[tex](M+m)v_2 = -m_v1[/tex]
[tex]v_2 = \frac{-Mv_1}{M+m}[/tex]
[tex]v_2 = \frac{-(46)(1.48)}{(157+46)}[/tex]
[tex]v_2 = -0.3353m/s[/tex]
Since the ice surface is frozen lake and girl is moving on it so the relative velocity will get added. Therefore the velocity of the girl relative to the ice surface is as,
[tex]v_1+v_2 = 1.48+(-0.33353)[/tex]
[tex]v_1+v_2 = 1.14647m/s[/tex]
The velocity of the girl relative to the ice surface is 1.14647m/s
PART B) The velocity of the plank plus girl is [tex]v_2 = -0.3353m/s[/tex]
Since the ice surface is frozen lake and plank is moving with girl on it so the relative velocity will get added. Therefore the velocity of the plank relative to the ice surface is as:
[tex]v_2 = -0.3353m/s[/tex]
"The correct answers are: (a) The girl's velocity relative to the surface of ice is 1.48m/s. (b) The velocity of the plank relative to the surface of ice is 0 m/s.
(a) Since the girl is walking on the plank with a constant velocity of 1.48 m/s relative to the plank, and the plank itself is at rest on the frictionless ice surface, there are no external forces acting on the girl-plank system in the horizontal direction.
According to the principle of inertia, an object at rest will stay at rest, and an object in motion will stay in motion with a constant velocity unless acted upon by an external force. Therefore, the girl's velocity relative to the surface of ice is the same as her velocity relative to the plank, which is 1.48 m/s.
(b) The plank is initially at rest on the frictionless ice surface, and since there are no external forces acting on it in the horizontal direction, it will remain at rest relative to the ice surface. This means that the velocity of the plank relative to the surface of ice is 0 m/s. The girl walking on the plank does not affect the plank's velocity because her motion is internal to the girl-plank system, and there is no friction to transfer her momentum to the plank.
In summary, the girl's motion is relative to the plank, and since the plank remains stationary on the ice, her velocity relative to the ice is the same as her walking velocity on the plank. The plank itself does not move because of the lack of friction and external forces, thus its velocity relative to the ice remains 0 m/s."
