Understanding the Range Equation of Projectile Motion

The Horizontal Range of a Projectile is defined as the horizontal displacement of a projectile when the displacement of the projectile in the y-direction is zero. This video explains how to use the equation, why a launch angle of 45° gives the maximum range and why complementary angles give the same range.

0:00 Intro
0:16 Defining Range
0:50 How can the displacement in the y-direction be zero?
1:21 The variables in the equation
2:09 g is Positive!
3:05 How to get the maximum range
4:17 What dimensions to use in the equation
5:19 The shape of the sin(θ) graph
6:17 sin(2·30°) = sin(2·60°)
7:35 A graph of the Range of various Launch Angles
8:18 The Review

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[blackfoxmp]

I've learned so much from watching your physics videos in two days than what I have failed to learn in a month from my incompetent physics professor. Thank you so much for posting such high-quality videos that are also entertaining! 

[ongguitar]

I had no idea what I was doing in this chapter and after watching your videos on kinematics and projectile motion, I was able to get a 100 on my unit test!! Thank you for these really explanatory videos!!

[dikachi]

Dude, you're a lifesaver. I've got a test tomorrow. Hope I pass

[Yh-gucw]

you should teach professors on how to teach physics.

[LimitDoesNotExistTutor]

I love how you sneak warnings for common mistakes into your videos. That situation where you forget to switch the calculator mode between your physics and calculus classes... 😭!

[thadeusaegeon]

OMG THANK YOU MR P!
My physics teacher right now is screwing me so hard so I started referring to your videos.

[allrounder]

Sir your explanation is too good . Thank you sir for this explanation

[brothergenesis]

How would you calculate the change in distance from a elevated launch platform?

[samuelhbean]

Billy's "and this one time" bit reminds me of Anthony Michael Hall's monologue about his cousin Kendall.

[Joker-lstq]

Dhanyawad. (Means THANKS in hindi).
Your FAN from india

[stovegamesgames]

This is a really good video! Made really easy to understand :D Plus I like the humor

[noarhaltallal]

Hello
I have a duty to Sunday and need your help I could not understand the question clearly

[killadaramu]

Professor can u say where you are. I mean which place

[fuelthefirefighters]

but how do you use the Range equation if you do not know the angle?? I have the initial velocity and where object lands ??

[ummeyhabiba]

can you please tell me that why do we use the derivative of something with respect to something to find the maximum quantity of that particular thing?

[harshithgowni]

Mr.P how do you stand Bo disrespecting you like at 2:09?

[bobbyfr]

Hey Mr. P, why did we use sin(2theta) in the range equation and not 2sin(theta)cos(theta)?

[rosealt]

I needed this so much ; O; Thanks lmao

[andreameigs]

I thought sin 2 theta is a trig identity that equals 2(sin theta cos theta).

[toobakabir]

if only i could give you more than one like