To solve this problem we will apply the concepts related to the conservation of the Momentum. The initial momentum must be equal to the final momentum. Momentum is described as the product between body mass and its respective velocity. Since there is no movement at the end of the collision, the final momentum will be zero.
Our values are given as
Mass of Cadillac
[tex]m_1 = 1000kg[/tex]
mass of VW
[tex]m_2 = 2000kg[/tex]
Let VW impact with speed v, then for conservation of momentum
[tex]m_1v_1+m_2v_2 = 0 \rightarrow[/tex] the Final speed is zero
Replacing,
[tex]1000kg*5mph+2000kg(-v) = 0[/tex]
[tex]v = \frac{1000kg*5mph}{2000kg}[/tex]
[tex]v = 2.5mph[/tex]
Therefore the speed to bring the cadillac to a halt is 2.5mph
The speed that can impact the Cadillac to bring it to a halt is 2.5 mph.
Velocity of the car can be calculated by the conservation of momentum formula,
[tex]\bold {m_1 v_1 =m_2v_2 = 0}[/tex] Since the final speed is zero,
where,
[tex]\bold {m_1 - mass\ of\ the\ cadillac = 1000 kg}\\\bold {m_2 - mass\ of\ the\ Volks\ Vagon = 2000 kg}[/tex]
[tex]\bold {v_1}[/tex] - velocity of the Cadillac - 5 mph.
Put the values in the formula
[tex]\bold {1000\ kg \times 5\ mph + 2000 kg (-v) = 0 }\\\\\bold {v = \dfrac {1000\ kg \times 5\ mph}{2000\ kg}}\\\\\bold {v = 2.5\ mph}[/tex]
Therefore, the speed that can impact the Cadillac to bring it to a halt is 2.5 mph.
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