A car with a mass of 950 kg and an initial speed of v1 = 21.5 m/s approaches an intersection, as shown in the figure. A 1300 kg minivan traveling northward is heading for the same intersection. The car and minivan collide and stick together. If the direction of the wreckage after the collision is 43.0° above the x axis.
Find the initial speed of the minivan and the final speed of the wreckage, m/s.
(950kg)(21.5)=(1300)(Vi van)
Vi van = (950*21.5)/1300
Vi Van = 15.71 m/s
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I don't know how to find the second part.
Can someone answer this ? I was here looking for that answer myself.
Never-mind above that's a wrong approach
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Let's assume that the initial speed of the minivan is v2.
Step 1: Find the momentum of the car before the collision.
Momentum of the car before the collision (p1) = mass of the car (m1) * initial speed of the car (v1)
p1 = 950 kg * 21.5 m/s
Step 2: Find the momentum of the minivan before the collision.
Momentum of the minivan before the collision (p2) = mass of the minivan (m2) * initial speed of the minivan (v2)
p2 = 1300 kg * v2
Step 3: Find the total momentum before the collision.
Total momentum before the collision = p1 + p2
Step 4: Find the final speed of the wreckage after the collision.
Using the conservation of momentum, the total momentum after the collision will be equal to the total momentum before the collision.
Total momentum after the collision = total momentum before the collision
Since the car and the minivan stick together after the collision, their masses combine.
Total mass of the wreckage (m) = mass of the car (m1) + mass of the minivan (m2)
Using trigonometry, we can find the horizontal and vertical components of the total momentum after the collision.
Horizontal component of the wreckage's momentum = final speed of the wreckage (v') * cosine of the angle (43°)
Vertical component of the wreckage's momentum = final speed of the wreckage (v') * sine of the angle (43°)
Finally, we can write the equation for the total momentum after the collision and solve for the final speed of the wreckage.
Total momentum after the collision = m * v'
By equating the total momentum before and after the collision, we can find the value of the final speed of the wreckage.
To solve this problem, we can apply the principles of conservation of momentum and conservation of kinetic energy.
Let's denote the initial speed of the minivan as v2 and the final speed of the wreckage as vf.
Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is given by the product of its mass and velocity. Therefore, we can write:
(mass of car * v1) + (mass of minivan * v2) = (mass of car + mass of minivan) * vf
Plugging in the given values:
(950 kg * 21.5 m/s) + (1300 kg * v2) = (950 kg + 1300 kg) * vf
Now, let's use conservation of kinetic energy. The kinetic energy before the collision is equal to the kinetic energy after the collision. The kinetic energy of an object is given by half the product of its mass and the square of its velocity.
(1/2) * (mass of car * v1^2) + (1/2) * (mass of minivan * v2^2) = (1/2) * (mass of car + mass of minivan) * vf^2
Plugging in the given values:
(1/2) * (950 kg * (21.5 m/s)^2) + (1/2) * (1300 kg * v2^2) = (1/2) * (950 kg + 1300 kg) * vf^2
Now we have a system of two equations with two unknowns (v2 and vf). We can solve this system of equations to find the values.
Simplifying the equations, we have:
1. Equation 1: 20425 + 1300v2 = 2250vf
2. Equation 2: 10286.25 + 650v2^2 = 1625vf^2
Using substitution or elimination method, we can solve these equations to find the values of v2 and vf.