# Projectile motion

#### DeltaForce

Gold Member
Homework Statement
Show that the range of the projectile is the same for two different projection angles --- a pair that add up to 90 degrees.
Homework Equations
theta1 +theta2 = 90

v^2 * sin(2theta1)/g = v^2 *sin(2theta2)/g
theta1 = 90- theta2
I substituted that into v^2*sin(2theta1)/g
So I get
v^2*sin(180-2theta2)/g

Now I'm stuck. What do I do next?

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#### scottdave

Homework Helper
You need to go back to the equation. You need to show that the 2 sides of the equation are indeed equal, using some trigonometric identities. You may find this list of identities helpful. https://bitly.com/trigiden

#### DeltaForce

Gold Member
Ohh... ok. So it has something to do with the sum and difference identities. Thank you.

#### haruspex

Homework Helper
Gold Member
2018 Award
What do I do next
You ought to know how to simplify sin(180-x), sin(90-x), sin(180+x), and likewise with cos.

#### DeltaForce

Gold Member
Yeah. I got it with the trig identities.

"Projectile motion"

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