Upward Projectile Motion (Which equation do I use?)

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A-linav

Homework Statement


Textbook problem 41: a football kicked at 35 m/s at 40 degrees to the ground, with parts a) how far it travelled, b) initial vertical and horizontal velocity components, c) horizontal distance and height of a javelin after 2.0 s.


Homework Equations


Equation: delta d_h = (v_i^2 sin 2theta) / a, a horizontal range formula for projectile motion.
Equation: Δd = v̄₁Δt + (1/2) ā Δt², a kinematics displacement formula with time-averaged velocity and acceleration terms.
Equation: delta d_h = v_h delta t, with delta d_h on the left, v_h on the right, and the subscript h marking the horizontal component.


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.

Handwritten physics work on lined paper showing two methods for finding a vertical displacement of 123 m from a 35 m/s launch at 40 degrees, with a small velocity triangle diagram at top.

Printed answers to problem 41: a) Δd_x = (20 m/s)² × sin80 / 9.8 m/s² = 40 m; b) vertical = 22.5 m/s, horizontal = 15.3 m/s; c) After 2.0 s, it had travelled 31 m horizontally and was 25 m above ground.
 
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A-linav said:
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.

A-linav said:
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.
A-linav said:
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.
 
haruspex said:
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 :)