0:00 A street light is mounted at the top of a 15-ft-tall pole 0:32 Draw a sketch 1:37 Come up with your equation 9:58 Implicit Differentiation 10:45 Solve For the Desired Rate of Change
I followed all of these steps and got the answer wrong. I think I'm going to go jump off a building. What is the rate of change of my falling speed if I jump off a building 11 stories high with an initial velocity of 5 m/s? For reference, I clock in at 5'10 and don't possess a shadow. What is the rate of change of the tip of my tip changing?
This comment was an obvious joke -- I found my error and corrected it after rewatching your tutorial. I apologize if the contents of the message were inappropriate or disturbing to anyone who read it, I've had a rough day and engineering is getting more daunting by the day.
Thank you very much for this video. It explained clear. But I have one question: The speed of shadow (dZ/dt) = 25/3 (ft/sec) is a constant. Shouldn't the speed of the tip of the shadow moving faster and faster as the man is moving further away from the pole, because the incline angle from the tip of shadow to the light gets smaller and smaller? So the speed of the shadow dX/dt should not be a constant. Right now, X = Z-Y. dX/dt = dZ/dt - dY/dt = 25/3 - 5 = 10/3 (ft/sec), which is a constant. Please clarify for me. Thank you very much.
It does seem like that might be the case, but the math confirms it is actually a constant speed. You could test this too by taking a few points in time and drawing what those triangles would look like. You would see that the tip of the shadow moves the same distance between t=1 and t=2 as it does between t=10 and t=11, or any other two time values that are the same distance in time from each other. Therefore its speed is constant.
You can’t plug in 40 for y before the implicit differentiation step because it’s changing over time. Any variables that are changing over time can’t be plugged in until after the implicit differentiation step. You can plug in constants, but y changes as the person walks, so it’s not a constant.
0:00 A street light is mounted at the top of a 15-ft-tall pole
0:32 Draw a sketch
1:37 Come up with your equation
9:58 Implicit Differentiation
10:45 Solve For the Desired Rate of Change
Taking differential calculus is hard working full time and not having lectures. You have helped me get a better understanding faster. Thank you.
That’s awesome, I’m happy to hear my videos helped. That is a tough thing to do. Keep up the good work!
Thank you so much! Was struggling with this on my hw and had no resources of help! You made this problem so easy 🤗🤗
AM LITERALLY CRYING RIGHT NOW. you made it look sooo simple. THANK YOU SOOO MUCH. i just subbed
Awesome! I’m glad it helped so much!
This really helped a lot. Thanks!
11 min long video = 1 hr long math lecture
Thank you, hope it helped!
hey man, we did a pop quiz in the middle of our class and you just saved my grade, have a good one
Awesome! I’m glad it helped!
Very helpful thank you!
That was so easy to follow ❤ thanks!
Thank you for this! The music was a nice touch.
Thank you! I’m glad you like it. I really liked the addition of some background music too!
Thank you so much!
You’re welcome!
Really well explained man, keep it up!!
I'm glad it helped!
Great presentation. Bravo keep up the great work!
Thank you, I will!
Awesome video! Thanks for the help!
Nick Weber you’re welcome!
I followed all of these steps and got the answer wrong. I think I'm going to go jump off a building. What is the rate of change of my falling speed if I jump off a building 11 stories high with an initial velocity of 5 m/s? For reference, I clock in at 5'10 and don't possess a shadow. What is the rate of change of the tip of my tip changing?
This comment was an obvious joke -- I found my error and corrected it after rewatching your tutorial. I apologize if the contents of the message were inappropriate or disturbing to anyone who read it, I've had a rough day and engineering is getting more daunting by the day.
Thank you very much for this video. It explained clear. But I have one question: The speed of shadow (dZ/dt) = 25/3 (ft/sec) is a constant. Shouldn't the speed of the tip of the shadow moving faster and faster as the man is moving further away from the pole, because the incline angle from the tip of shadow to the light gets smaller and smaller? So the speed of the shadow dX/dt should not be a constant. Right now, X = Z-Y. dX/dt = dZ/dt - dY/dt = 25/3 - 5 = 10/3 (ft/sec), which is a constant. Please clarify for me. Thank you very much.
It does seem like that might be the case, but the math confirms it is actually a constant speed. You could test this too by taking a few points in time and drawing what those triangles would look like. You would see that the tip of the shadow moves the same distance between t=1 and t=2 as it does between t=10 and t=11, or any other two time values that are the same distance in time from each other. Therefore its speed is constant.
thanks bro you helped a lot
You’re welcome, happy to hear that!
amazing explanation
You solve my calc hw, tysm
You’re welcome!
Great video!!, Can I have the music name around 6:00 ? I really like the music
Honestly, I can't remember which song it is unfortunately. I got it on epidemicsound.com though.
why do we take it from all the part of the triangle like the x and y and not just the y part
?
thank you so much man
You’re welcome!
thank you
You’re welcome!
So, no use of y=40 then?
why is dy/dt 5? is that is x
why couldnt we just replace the y variable with 40?
You can’t plug in 40 for y before the implicit differentiation step because it’s changing over time. Any variables that are changing over time can’t be plugged in until after the implicit differentiation step. You can plug in constants, but y changes as the person walks, so it’s not a constant.
should remove the back ground music next time
Thank you for the feedback, I appreciate that. Did you find the music distracting? Was it just too loud?
Jake's Math Lessons I found it a little bit distracting
Thanks for the heads up!
@@JakesMathLessons you did a great job explaining though!!
@@saeroyipark6047 thank you!