First slide

Collisions

Question

A car of mass 500kg(including the mass of a block) is moving on a smooth road with velocity 1.0 $m s^{- 1}$ along positive x-axis. Now a block of mass 25kg is thrown outside with absolute velocity of 20 $m s^{- 1}$ along positive z-axis. The new velocity of the car is ( $m s^{- 1}$ )

Moderate

A

$10 \hat{i} + 20 \hat{k}$
B

$10 \hat{i} - 20 \hat{k}$
C

$\frac{20}{19} \hat{i} - \frac{20}{19} \hat{k}$
D

$10 \hat{i} - \frac{20}{19} \hat{k}$

Solution

$\begin{array}{l} {\vec{P}}_{i} = {\vec{P}}_{f}, i n i t i a l m o m e n t u m = f i n a l m o m e n t u m, f r o m c o n s e r v a t i o n p r i n i c p l e o f l i n e a r m o m e n t u m \\ {(m_{c a r + b l o c k} v)}_{i n i t i a l} = {{(m v_{})}_{b l o c k} + {(m_{r e m a i n i n g} v_{})}_{c a r}}_{f i n a l} \\ ∴ (500) (1) (\hat{i}) = (25) (20 \hat{k}) + 475 \vec{v} \\ ∴ f i n a l v e l o c i t y o f c a r i s \vec{v} = [(\frac{20}{19} \hat{i}) - (\frac{20}{19} \hat{k})] m / s \end{array}$

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