7:05 Mr. P, if range is described as the displacement in the x direction when the displacement in the y direction is zero, then what will it be if the displacement in the y direction is not zero and either is positive or negative?
You said "range" is the distance of x direction, but why did you substitute time taken in 'y' direction to the range equation?? (5: 20 to 5:25) I didn't understand that!!! Plz clear it..
By definition of the conditions of the range equation, the displacement in the y-direction adds up to zero, because it starts and ends at the same vertical position. The x-position is what changes. We get the x-direction equation of motion from v0*cos(theta) * delta_t. Constant velocity kinematics. We use the y-direction equation of motion from constant acceleration kinematics, and use it to solve for delta_t. y = -1/2*g*delta_t^2 + v0*sin(theta)*delta_t. Set y=0 when delta_t equals the value of interest, and solve for delta_t.
" I want to feed cattle when I grow up" - me "Get a degree for it and make the big bucks" - mom " R = vi squared sin 2 theta divided by g."- professor " I said FEED cattle, not FIRE cattle OUT OF CANNONS"
@@LinkinPark15Ash because wind resistance would reduce accuracy of point of impact from point of aim. If I increase the density of the projectile, the biggest pig of the cattle heard would eat it all... Also gunpowder is expensive. Mostly gun powder is expensive.
The reason the double angle formula occurs, is that we end up with sin(theta)*cos(theta) in our equation. In order to simplify this expression so that there is only one instance of theta, we use trig identities to replace it with the equivalent expression, since sin(theta)*cos(theta) = sin(2*theta)/2. This makes it easier to solve for special points, like what value of theta gives the maximum range? Answer: 45 degrees. Or given a particular range of a projectile, what two possible launch angles will enable it to complete this range? It is true that the double angle trig identity is usually expressed as the following in reference tables: 2*sin(theta)*cos(theta) = sin(2*theta) However, you can multiply both sides by 1/2, to make it look like the expression we have in this derivation. 1/2 * 2*sin(theta)*cos(theta) = 1/2 * sin(2*theta) Thus: sin(theta)*cos(theta) = sin(2*theta)/2
If not otherwise specified with context, g is positive. In this particular problem, we define up as the +y direction. The object must accelerate downward because downward is defined in the direction of gravity. This means that the acceleration is in the -y direction. It's magnitude is equal to g, and therefore, ay = -g.
+AlchemistOfNirnroot I also do A Level Maths, so I'm more than comfortable with double angle formulae, however this is a first year paper (we learned the trig identity in second year) which I'm retaking this month : o
I dared my dad, if he could derive it and he did and then he dared me if I could derive in different method. Your video came from heaven when I was I in hell
I love this video. I didn't learn anything though because I was too caught up watching all of your characters interact. LOL. Too funny.
I guess you will have to watch it again. 😊
@softbreezy That's risible 😂!
WOW!
I really like the editing and the teaching technique, he resembles as if he was teaching a class
Thanks! 😃
i'm a 3rd year marine eng. i watched the video and helped me a lot ,thanks
You are very welcome!
Creative & Easy to understand - Thank You Sir.
You are welcome!
Really easy to understand. I started loving physics after watching these videos.
Great!
Currently stressing over test tomorrow rewatching this. THANK YOU 🙏
THANK YOU for being an inspiration to others. you motivate us to work harder and learn more. You're the best !
+Chary Nud "you motivate us to work harder and learn more" is high praise. Thanks!
Loved the way of your teaching 👍🏻👍🏻👍🏻
Great!
7:05 Mr. P, if range is described as the displacement in the x direction when the displacement in the y direction is zero, then what will it be if the displacement in the y direction is not zero and either is positive or negative?
very helpful video!!!! lol i also loved how all three of the students were wearing the same socks
Why do you divide by Δt at 4:10?
You said "range" is the distance of x direction, but why did you substitute time taken in 'y' direction to the range equation?? (5: 20 to 5:25) I didn't understand that!!! Plz clear it..
By definition of the conditions of the range equation, the displacement in the y-direction adds up to zero, because it starts and ends at the same vertical position. The x-position is what changes.
We get the x-direction equation of motion from v0*cos(theta) * delta_t. Constant velocity kinematics.
We use the y-direction equation of motion from constant acceleration kinematics, and use it to solve for delta_t. y = -1/2*g*delta_t^2 + v0*sin(theta)*delta_t. Set y=0 when delta_t equals the value of interest, and solve for delta_t.
You guys are awesome. Thank you for the helpful video. Awesome video by the way.
I will accept your compliment on behalf of all of "you guys", thanks.
+Slayther Morderclaw That's quite awesome, thanks!
This video was great, I actually understand it now THANKYOU
+Joanna Cheng You are welcome. Helping you understand physics is my goal. Glad to know I am being successful!
" I want to feed cattle when I grow up" - me
"Get a degree for it and make the big bucks" - mom
" R = vi squared sin 2 theta divided by g."- professor
" I said FEED cattle, not FIRE cattle OUT OF CANNONS"
why not fire the feed out of cannons to the cattle? lol
i mean ur feeding the cattle to the cannons aren't u?
@@LinkinPark15Ash because wind resistance would reduce accuracy of point of impact from point of aim. If I increase the density of the projectile, the biggest pig of the cattle heard would eat it all... Also gunpowder is expensive. Mostly gun powder is expensive.
@@UnknowableDandelion if that's a joke, I don't get it.
Edit. Nevermind. It just took me a minute.
@@ricknerinfantry :)
This video is soooo helpful! Thank you for it!!
You are soooo welcome! Thanks for your kind words.
bro u r the best, by watchin gur videos I got a 93 in my practice AP Physics 1 test. thank you for ur hard work
+Ahmad N. Sakib CHowdhury You keep up your good, hard work. Sounds like you will do well on the exam.
THanks a bunch!
This is a fantastic video
plz how could u use the Sine Double Angle Formula if you only have Sin θ_i Cos θ_i and not 2Sin θ_i Cos θ_i
The reason the double angle formula occurs, is that we end up with sin(theta)*cos(theta) in our equation. In order to simplify this expression so that there is only one instance of theta, we use trig identities to replace it with the equivalent expression, since sin(theta)*cos(theta) = sin(2*theta)/2. This makes it easier to solve for special points, like what value of theta gives the maximum range? Answer: 45 degrees. Or given a particular range of a projectile, what two possible launch angles will enable it to complete this range?
It is true that the double angle trig identity is usually expressed as the following in reference tables:
2*sin(theta)*cos(theta) = sin(2*theta)
However, you can multiply both sides by 1/2, to make it look like the expression we have in this derivation.
1/2 * 2*sin(theta)*cos(theta) = 1/2 * sin(2*theta)
Thus:
sin(theta)*cos(theta) = sin(2*theta)/2
at the end of the video, why g is negative?isn't it supposed to negative because of the downward acceleration. can anyone help me ouT?
If not otherwise specified with context, g is positive. In this particular problem, we define up as the +y direction. The object must accelerate downward because downward is defined in the direction of gravity. This means that the acceleration is in the -y direction. It's magnitude is equal to g, and therefore, ay = -g.
thanks my classical mechanics class had a hw problem like this.
Helped a lot, thanks :-)
I'm from the UK, doing A Level Physics. Just wondering if this question ever came up, do you reckon they'd tell you sin2A=sinAcosA?
+AlchemistOfNirnroot I also do A Level Maths, so I'm more than comfortable with double angle formulae, however this is a first year paper (we learned the trig identity in second year) which I'm retaking this month : o
Thank You!
U r awesome sir
+Gholam Mustafa Ali Glad you think so. How many of my videos have you watched in the last 2-3 days?
thanks dawg
You are welcome.
very nice
Thanks guys
You are welcome.
Please try to make it a bit slower next time while explaining about the formulas
Its too fast for me to understand
thank you so much though
I dared my dad, if he could derive it and he did and then he dared me if I could derive in different method. Your video came from heaven when I was I in hell
Glad to help!