Changing from parametric form to algebraic form

[Burr2]

X1 T = 10T

Y1 T = 100 + (.5 * -9.8T^2)

X2 T = 100 - 12.3 T

Y2 T = 0

How do I put this into algebraic form? it seems easy but I just can't get it.

 

[andrevdh]

It seems these four equations describes the positional coordinates of two different objects as functions of time.

So what do you need to determine about these two objects?

 

[kyle8921]

To change from parametric form to algebraic form, we need to eliminate the parameter (in this case, T) and express the equations in terms of the variables (in this case, X and Y).

For X1 T = 10T, we can divide both sides by T to get X1 = 10. This is the algebraic form of the first equation.

For Y1 T = 100 + (.5 * -9.8T^2), we can first multiply both sides by 2 to get 2Y1 T = 200 - 9.8T^2. Then, we can rearrange the terms to get 9.8T^2 + 2Y1 T - 200 = 0. This is a quadratic equation in terms of T, but we want to express it in terms of Y. To do this, we can use the quadratic formula to solve for T in terms of Y. This will give us T = (-2Y1 ± √(4Y1^2 - 4(9.8)(-200)))/2(9.8). Simplifying this gives us T = (-Y1 ± √(Y1^2 + 4900))/9.8. We can now substitute this value of T into the original equation to get an algebraic form of Y1 in terms of Y: Y1 = 100 + (.5 * (-Y1 ± √(Y1^2 + 4900))/9.8)^2.

For X2 T = 100 - 12.3 T, we can divide both sides by T to get X2 = 100/T - 12.3. This is the algebraic form of the third equation.

For Y2 T = 0, we can simply state that Y2 = 0. This is the algebraic form of the fourth equation.

Overall, the equations in algebraic form would be:

X1 = 10
Y1 = 100 + (.5 * (-Y1 ± √(Y1^2 + 4900))/9.8)^2
X2 = 100/T - 12.3
Y2 = 0