Crash Momentum: 1500kg Boulder, 500kg Truck

In summary, the problem involves a 1500 kg boulder moving at 10m/s in a Westerly direction colliding with a 500kg truck moving at 20m/s at a direction of S30°W. After the collision, the boulder moves away at 5m/s in a direction of S70°W. The goal is to find the speed and direction of the truck after the crash. The equations used are for horizontal and vertical components, which result in a value of 20° for the direction of the truck.
  • #1
Tankertert
4
0

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!
 
Last edited:
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  • #2
Tankertert said:
[

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°.
 

1. How does the boulder's momentum compare to the truck's momentum in this crash?

The boulder's momentum is three times greater than the truck's momentum. This is because momentum is mass multiplied by velocity, and the boulder has three times the mass of the truck.

2. What is the overall kinetic energy of the boulder and truck before the crash?

The overall kinetic energy of the boulder and truck before the crash is determined by adding the individual kinetic energies of each object. This is calculated by using the equation KE = 1/2 * m * v^2, where m is the mass and v is the velocity.

3. How does the truck's mass affect the outcome of the crash?

The truck's mass plays a significant role in determining the outcome of the crash. In this scenario, the truck's smaller mass means it has less momentum and kinetic energy compared to the boulder. This results in the truck experiencing a greater force and potentially sustaining more damage in the crash.

4. Would the outcome of the crash be different if the boulder and truck were traveling at different velocities?

Yes, the outcome of the crash would be different if the boulder and truck were traveling at different velocities. This is because momentum is directly proportional to velocity, so a change in velocity would result in a change in momentum and ultimately, the outcome of the crash.

5. How do other factors, such as friction and air resistance, affect the crash?

Factors such as friction and air resistance can affect the crash by slowing down the objects and reducing their momentum and kinetic energy. This can result in a less severe crash compared to a scenario with no external forces acting on the objects. However, these factors can also potentially cause the objects to change direction or spin, altering the outcome of the crash.

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