Crash Momentum: 1500kg Boulder, 500kg Truck

[Tankertert]

Homework Statement

A boulder that weighs 1500 kg is moving 10m/s in a Westerly direction, until it collides with a truck of mass 500kg traveling at 20m/s at a direction S30°W. After the collision the boulder moves away at 5m/s at a direction of S70°W. Find the speed and direction of the truck adter the crash.

Homework Equations

The Attempt at a Solution

I tried sorting the problem into horizontal and vertical aspects.

the horizontal equation looks like:

1500 * -10 + 500(-20 cos 60) = 1500 * (-5 cos 30°) + 500(v cos θ)

which solves to: v cos = -34.38

where the 1500 and the 500 are the masses, the (-10) and (-5 cos 30) are the before the crash horizontal vectors, and (-20 cos 60) and (v cos θ) the after crash horiz vectors.

the vertical equation:

1500 * 0 + 500(-20 sin 60) = 1500 * (-5 sin 30) + 500( v sin θ)

which solves to: v sin θ = -9.82

where 1500 and 500 are the masses again, (0) and (-20 sin 60) the before the crash vertical components, andd (-5 sin 30) & (v sin θ) the after the crash components.

from here i tried:

tan θ = -34.38 / -9.82
θ = 0.061

but I am fairly certain this is wrong. Can anyone please tell me where i went wrong? thank you!

 

[azizlwl]

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The Attempt at a Solution

I tried sorting the problem into horizontal and vertical aspects.

the horizontal equation looks like:

1500 * -10 + 500(-20 cos 60) = 1500 * (-5 cos 30°) + 500(v cos θ)

which solves to: v cos = -34.38

!

It should be 20°.