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#1 2016-10-23 07:53:38

markosheehan
Member
Registered: 2016-06-15
Posts: 51

projectile

a particle is projected from ground level with initial speed 8i+28j m/s. find the two times when its speed will be 10 m/s. i tried working this out by this.

√(8²+(21-gt)²)=100  (by the way the square root goes over it all even though it doesnt look like it) but when i solved for t i did not get the right answer. the right answer is   110/49 and 170/49.

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#2 2016-10-23 10:12:41

Lehona
Member
Registered: 2016-10-22
Posts: 16

Re: projectile

You made two mistakes in your formula: a) You used 21 instead of 28 and b) you used 100 instead of 10 (you can use 100 if you leave out the square root).

I assume that 28 is the vertical velocity (it looks like it in your approach).

Then we get: v(t) = 8i+(28-gt)
speed(t) = |v(t)| = sqrt(8²+(28-gt)²) = 10
8²+(28-gt)² = 100
(28-gt)² = 36
784-56gt+g²t² = 36
748-56gt+g²t² = 0

Just plug that into any formula for solving quadratics of your liking

If we set g as 9.8 you get exactly the answers given.

Last edited by Lehona (2016-10-23 10:13:50)

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#3 2016-10-23 17:43:34

Member
Registered: 2016-04-16
Posts: 1,086

Re: projectile

Last edited by thickhead (2016-10-24 02:10:07)

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#4 2016-10-24 01:18:39

Lehona
Member
Registered: 2016-10-22
Posts: 16

Re: projectile

Just a suggestion, but v and u are nearly impossible to distinguish in LaTeX, I'd usually avoid using them both at the same time.

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#5 2016-10-24 02:10:58

Member
Registered: 2016-04-16
Posts: 1,086

Re: projectile

I hope it is clear now.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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