Determine the minimum initial velocity v0 (solved)

Determine the minimum initial velocity v0 and the corresponding angle θ at which the ball must be kicked in order for it to just cross over the 3-m high fence.

Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2013.

[wt]

Love how you made notes and posted them in the description. Really appreciate the commitment :)

[muhammadsaboor]

Finally ..a very much clear explaination ...

[dxfootball]

Please at 2:14 can you explain why you added 180?
And will the answer be same if you use the -63.43 like that?

[sohcahtoa]

Hi, I am currently creating a robot that would always be able to shoot basketballs into the basket given initial height, final height and final distance( final height and distance would be the x, y location of the basket). I was planning on using a constant angle of 45 degrees because of how simple it is to simplify the equation due to cos and sin being equal. I came up with the equation of v0 = ((- 9.81 * x^2)/(y - y0 - x))^0.5 . I'm considering using this method due to how it decreases the v0 but I'm still learning and I want the equation to be simple. What do you think, do you believe I should use an angle of 45 degrees and just adjust the x component or should I use this method to minimize power needed but make it a bit more complex. Sorry about how wordy this was but I will appreciate any feedback that comes my way. Thanks in advance!

[hudahelmiyazar]

Hi may I know why the derivative must be equal to 0? Thanks in advanced.

[DataPotato]

Hey is there a formula for this? If so can you tell me what the formula is?

[eiao]

Concise and understandable, thank you!

[joonok]

This way of solving is very specific, it wont work if an integer is left over on a component. Very important you check out the notes on how he solved it

[adriansagnip]

What must be the initial velocity to reach 1000m range? What is the total time to reach this range?

[apoorv]

There is one more way of solving this but that would be a bit tedious. Forming quadratic in tan theta in projectile motion path equation such that its determinant is greater than zero. Basically that would give an inequality in velocity

[chrischan]

Are you still active? Can I ask a question? How did you get -63.43? Thanks for the fast response.

[angelineromanbautista]

Minimum initial velocity? Is there a maximum initial velocity? or you mean just the initial velocity itself?

[elieghanem]

Hello i understood everything but why is the denominator a maximum for a derivative=0?

[sevionlyfans]

Hello, can you teach how to solve for initial velocity when the only given is time, displacement, and angle? Thank you!

[fireblitz]

how would this work if you had the angle from the start

[byvikam]

I tried solving this by setting 0 = v0*sinθ - gt, since for v0 to be the smallest, the maximum height should be 3 meters. However, this did not give me the right answer. I do not understand why this does not give the correct result?

[princesspat]

Im a newbie to physics...Why did you take the derivative?

[leonardoantonio]

I need an answer for this: create an illustration when dela cruz kicked the ball at an angle of 60° with initial velocity of 20 m/s. Help me plss😭

[sarahaeeoof]

in simplifying it, why did u multiply it to 2?

[kayealwayssleep]

Thank you Sir! Simple and understandable ♥