Substituting t in Y-Coordinate: Exploring Answers

[bentley4]

In this solution the t in the y-coordinate equation is substituted using the x-coordinate equation and ultimately leads to the answer.

My questions:
1. Why don't I get the same answer when I substitute the v or v and t instead?
2. How am I supposed to know to substitute t in this example and not v?

 

[Delphi51]

I don't see how you can get it by keeping the t. You don't know t, so how can you tell the maximum value of x that way? I get
x = gt²/(2*tanΘ)
and can't tell what combination of t and Θ provide the maximum x.
It would be good to see your calc.

There is no need to eliminate the v; it is a constant. But you must eliminate the variable t.

 

[physicsisgrea]

Well, the problem is quite easy to approach.
Range is given by u^2 sin(2a) / g, where a is the projection angle.
Since -1<sin a<1, the max. value for a sine function = 1. This occurs when the angle is 90 degrees or .5pi radians.
So, for a fixed u:
2a = 90
a = 45 degrees.

 

[bentley4]

I don't see how you can get it by keeping the t. You don't know t, so how can you tell the maximum value of x that way? I get
x = gt²/(2*tanΘ)
and can't tell what combination of t and Θ provide the maximum x.
It would be good to see your calc.

There is no need to eliminate the v; it is a constant. But you must eliminate the variable t.

Ok, now I understand. Thnx!

 

[asteriatic]

1. The reason you may not get the same answer when substituting v or v and t instead of just t is because the equations may not be equivalent. The substitution of t in the y-coordinate equation may only work because the x-coordinate equation is a function of time, while the v and t equation may not have that same relationship. It is important to carefully analyze the equations and understand their relationships before making substitutions.

2. In this particular example, it seems that substituting t in the y-coordinate equation is the most logical option since the x-coordinate equation is a function of time. However, in other situations, it may be necessary to substitute different variables depending on the relationships between the equations. It is important to have a thorough understanding of the equations and their meanings in order to determine the most appropriate substitutions. Additionally, it may be helpful to consult with colleagues or do further research to gain a better understanding of the equations and their relationships.