Joint Variation: Collision impact of an automobile varies

christie_11

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Collision impact of an automobile varies jointly as its mass and the square of its speed. Suppose a 2000lb car was traveling 55mph has a collision impact of 6.1. What is the collison impact of the same car at 65mph?

I realize that its a joint variation, for which the equation is "y = kxz", right? I'm setting up the problem:

. . .2000 = 55(6.1)
. . .2000 = 335.5

Then I divide by 335.5 and get k = 5.9

I do not understand how to get the second part, y = 5.9xz, because I get a really large number.
 
christie_11 said:
2000 = 335.5
Two thousand is NOT equal to three hundred and some, and you cannot solve for "k" when there is no "k" in your equation. So what are you doing...?

Please clarify. Thank you.

Eliz.
 
As far as I know, I am supposed to solve for K, finding the collision impact for a car traveling 65mph.
K, is in the problem.
y=kxz

2000 divided by 335.5 = 5.9
K=5.9

I was able to set up the first part of the problem, just not the 2nd part. Solving for Y.
y=5.9 (?) (?)
But maybe Im even doing that part wrong.
The other example is simular, i use the same method but get a really big #.
 
christie_11 said:
Collision impact of an automobile varies jointly as its mass and the square of its speed. Suppose a 2000lb car was traveling 55mph has a collision impact of 6.1. What is the collison impact of the same car at 65mph?

I realize that its a joint variation, for which the equation is "y = kxz", right?
What does "y" stand for? What does "x" stand for? What does "z" stand for? Where do you account for the speed being squared? Where do you account for the variation constant, "k"?

christie_11 said:
I'm setting up the problem:

. . .2000 = 55(6.1)
Your equation (above) says "mass equals speed times impact", which is not the relation given in the exercise. Also, this does not account for the squaring, does not include the variation constant, and is a false statement (since 2000 does not equal 335.5).

Variation statements translate as follows:

. . . . ."y varies directly as x": y = kx
. . . . ."y varies inversely as x": y = k/x
. . . . ."y varies jointly as x and z": y = kxz

Try following the instructions in the exercise, and defining your variables clearly.

Eliz.
 
6.1 = k(2000)(55<sup>2</sup>)

k = 6.1/[(2000)(55<sup>2</sup>)]

now find the desired impact value for 65 mph.


an easier method ...

let x = desired impact value for 65 mph ...

x = k(m)(65<sup>2</sup>)
------------------------------------
6.1 = k(m)(55<sup>2</sup>)

divide the top equation by the bottom equation ...

x/6.1 = (65<sup>2</sup>)/(55<sup>2</sup>)

x = 6.1*(65<sup>2</sup>)/(55<sup>2</sup>)
 
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