Upward Projectile Motion (Which equation do I use?)

[A-linav]

Homework Statement

Homework Equations

The Attempt at a Solution

This is just for (a) as I have not attempted the others yet. Okay so my question is: How do I know which method/equation to use when finding the range of upward projectiles? Does it matter? I seem to have gotten the same answer (Dh= 123m) for both methods but my textbook didn't explain when to use which equation.
As well... Is my answer even correct? The answer in the textbook says the displacement is 40m but I don't know where they are getting this number.

 

[haruspex]

How do I know which method/equation to use when finding the range of upward projectiles?

Both are valid. The "range" equation you used in method 2 is proved using method 1.

my textbook didn't explain when to use which equation.

As long as the conditions for the range equation are met, you can use it. It gets more complicated when you want the range on an inclined plane, but again, there is an equation you can learn for that.
I was never very confident learning equations, but I could always remember how to derive them.
In the present case, method 1 answers part b as a side benefit.

The answer in the textbook says the displacement is 40m

The textbook has used 20 m/s as the launch speed.
This is a clear example of a question that has been sloppily modified. In part c, the football has turned into a javelin.

 

[A-linav]

Both are valid. The "range" equation you used in method 2 is proved using method 1.As long as the conditions for the range equation are met, you can use it. It gets more complicated when you want the range on an inclined plane, but again, there is an equation you can learn for that.
I was never very confident learning equations, but I could always remember how to derive them.
In the present case, method 1 answers part b as a side benefit.

The textbook has used 20 m/s as the launch speed.
This is a clear example of a question that has been sloppily modified. In part c, the football has turned into a javelin.

Thanks for your help and for your quick reply! I guess it just depends what is given in the question then :)