The wreckage moves in the direction 48° N of E just after the collision
[tex]\texttt{ }[/tex]
Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
Given:
mass of car 1 = m₁ = 900 kg
initial velocity of car 1 = u₁ = 15 i m/s
mass of car 2 = m₂ = 750 kg
initial velocity of car 2 = u₂ = 20 j m/s
Asked:
final velocity = v = ?
Solution:
Firstly , we will use Conservation of Momentum Law as follows:
[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex]
[tex]900(15 \widehat{i}) + 750(20 \widehat{j}) = 900v + 750v[/tex]
[tex]13500 \widehat{i} + 15000 \widehat{j} = 1650v[/tex]
[tex]v = (13500 \widehat{i} + 15000 \widehat{j}) \div 1650[/tex]
[tex]v = \frac{90}{11} \widehat{i} + \frac{100}{11} \widehat{j}[/tex]
[tex]\texttt{ }[/tex]
Next , we could find the direction of this final velocity as follows:
[tex]\theta = \tan^{-1} \frac{v_y}{v_x}[/tex]
[tex]\theta = \tan^{-1} \frac{100/11}{90/11}[/tex]
[tex]\theta = \tan^{-1} \frac{10}{9}[/tex]
[tex]\theta \approx 48^o \texttt{ N of E}[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{ }[/tex]
Grade: High School
Subject: Physics
Chapter: Dynamics
[tex]\texttt{ }[/tex]
Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
