Question

A 1460 kg car moving north at 27.0 m/s collides with a 2165 kg car moving east at 18.0 m/s. They stick together. In what direction and with what speed do they move after the collision?

Answer in degrees north of east
AND
the speed after the collision in m/s​

Answer 1

Solution given:

North car

mass[m1]=1460kg

velocity[u1]=27 m/s

mass[m2]=2165kg

velocity [u2]=18m/s

let v be velocity after collision

we have

From the principle of conservation of linear momentum

m1u1+m2u2=(m1+m2)v

1460*27+2165*18=(1460+2165)v

v=
`(78390)/(3625)`

v=21.6m/s

the speed after the collision in 21.6 m/s.

For angle.

Tan angle =
`(m1u1)/(m2u2)`

Tan angle =
`(1460*27)/(2165*18)`

Tan angle=327.74

angle=Tan-¹(327.74)=89.82=90°

in degrees north of east is 90°