Question

A 1500-kg car traveling east with a speed of 25.0 m/s collides at an intersection
with a 2500-kg van traveling north at a speed of 20.0 m/s. Find the direction and
magnitude of the velocity of the wreckage after the collision, assuming the vehicles
stick together after the collision.​

Answer 1

$\LARGE\sf{ Answer }$

From conservation of momentum :

Initial momentum = Final momentum

$\tt{ m }$$\tt\overrightarrow{u}$ + $\tt{ M }$$\tt\overrightarrow{u}$ = $\tt{ (m+M) }$$\tt\overrightarrow{u}$

$\tt{ 1500 × 25 }$$\tt\widehat{i}$$\tt{ +2500 × 20 }$$\tt\widehat{j}$$\tt{ (1500+2500) }$$\tt\overrightarrow{V}$

$\tt\overrightarrow{v}$$\tt{ = 9.375}$$\tt\widehat{i}$$\tt{ +12.5}$$\tt\widehat{j}$

$\therefore$ Final velocity when they stick together is $\tt{ 9.375 }$$\tt\widehat{i}$$\tt{ +12.5 }$$\tt\widehat{j}$