Finding Time in Projectile Motion

[fcb]

Homework Statement

A soccer ball is resting on a level football field is kicked, landing 20m away after 1.5 seconds. Neglecting the effects of spin and air resistance, Determine: The time when it was 2m above the ground

Homework Equations

U_x=13.333m
U_y=7.35m
t=?
(delta)y=2m
a_y=-9.8ms^-2

(delta)y=u_yt + 0.5a_yt²

The Attempt at a Solution

2=7.35t-4.9t²
t=5.35/4.9

EDIT: Upwards is taken to be +ve

~1.09

But that's not the answer in the book

 

[aurao2003]

Hi
Can you kindly explain how you obtained the horizontal and vertical velocity? Its seems that 20m is the range and the time of flight is 1.5s. Would the horizontal velocity be 3m/s? Please comment.

 

[tiny-tim]

hi fcb!

fine down to here …

2=7.35t-4.9t²
t=5.35/4.9

but you've spoiled it by reading it as if it was 2t on the left!

 

[fcb]

Would I have to use the quadratic formula to solve it?

 

[tiny-tim]

(just got up :zzz: …)

Yup!

 

[fcb]

Ohh early start I would gather. Anyways, is the quadratic formula the only way it can be done?

 

[tiny-tim]

either that, or https://www.physicsforums.com/library.php?do=view_item&itemid=107"

(why, don't you like the quadratic formula?)

 

[fcb]

It's not that i Don't like it, I was just curious to an extent. But when you rearrange it, why is it the one with t^2 the one that's represented as 'a' and the one with 't' alone represented as b in the equation for the quadratic formula. I know it is but why. I know nothing about maths or physics.

 

[tiny-tim]

because ax² + bx + c = a(x² + bx/a + c/a)

= a((x + b/2a)² - b²/4a² + 4ac/a²),

so x + b/2a = ±√(b² - 4ac)/2a

 

[fcb]

Thanks so much tiny-tim, You're a absolute legend