Kinematics: Range doubt - iTeachChem

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iTeachChem Helper

I

iTeachChem Helper•2/10/25, 4:00 AM

@Gyro Gearloose

iTeachChem Helper

I

iTeachChem Helper•2/10/25, 4:00 AM

Note for OP

+solved @user1 @user2...

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to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.

Nimboi

N

Nimboi•2/10/25, 4:03 AM

the frog jumps at what angle? the range depends on the angle right

SirLancelotDuLac

SSirLancelotDuLac How to go about option (3) & (4)? I have a vague-ish idea it has something to do...

Opt

O

Opt•2/10/25, 4:03 AM

Yeah, you're right. The radius of curvature is the radius of the circle that passes through the point on the trajectory and is tangent to the trajectory at that point, ie, the path can be locally approximated by the circle. So, the cylinder cross section is that circle for the highest point on the trajectory.

Nimboi

N

Nimboi•2/10/25, 4:03 AM

it could've jumped when close to the pipe (high angle), far from the pipe (low angle)

Opt

O

Opt•2/10/25, 4:03 AM

So using that, you can get the horizontal component of velocity

Opt

O

Opt•2/10/25, 4:03 AM

After which it is simple.

SirLancelotDuLac

S

SirLancelotDuLacOP•2/10/25, 4:05 AM

Yeah I got:

ucos(theta)>sqrt(rg)
Time of flight is (a), so usin(theta) can be found from there.

Nimboi

N

Nimboi•2/10/25, 4:05 AM

ah, ok i was tripping

SirLancelotDuLac

S

SirLancelotDuLacOP•2/10/25, 4:06 AM

But multiplying the time of flight and 1 doesn't give any option

Nimboi

NNimboi ah, ok i was tripping

SirLancelotDuLac

S

SirLancelotDuLacOP•2/10/25, 4:06 AM

Yeah. The highest point condition must be satisfied

SirLancelotDuLac

SSirLancelotDuLac But multiplying the time of flight and 1 doesn't give any option

Opt

O

Opt•2/10/25, 4:20 AM

Take FOR of cylinder.

Edit: COM of cylinder

Opt

O

Opt•2/10/25, 4:21 AM

Ignore rotation

SirLancelotDuLac

S

SirLancelotDuLacOP•2/10/25, 4:22 AM

Ah.

SirLancelotDuLac

S

SirLancelotDuLacOP•2/10/25, 4:23 AM

Oh right that gives (4) ig.

SirLancelotDuLac

S

SirLancelotDuLacOP•2/10/25, 4:23 AM

+solved @Opt @Nimboi

iTeachChem Helper

I

iTeachChem Helper•2/10/25, 4:23 AM

Post locked and archived successfully!

Archived by

@1075951732460376214 (1075951732460376214)

Time

February 10, 2025

Solved by

@763645886500175892 (763645886500175892), @717724055217635398 (717724055217635398)