Finding Time in Projectile Motion

AI Thread Summary
A soccer ball kicked on a level field lands 20m away in 1.5 seconds, prompting a calculation for the time it reaches 2m above the ground. The initial horizontal and vertical velocities are determined to be 13.333 m/s and 7.35 m/s, respectively. The equation used is 2 = 7.35t - 4.9t², leading to a solution for time using the quadratic formula. There is a discussion about the interpretation of the equation and the roles of coefficients in the quadratic formula. The conversation highlights confusion around the math but ultimately seeks clarity on the physics involved.
fcb
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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


Ux=13.333m
Uy=7.35m
t=?
(delta)y=2m
ay=-9.8ms-2

(delta)y=uyt + 0.5ayt2

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
 
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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.
 
hi fcb! :wink:

fine down to here :smile:
fcb said:
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! :cry:
 
Would I have to use the quadratic formula to solve it?
 
(just got up :zzz: …)

Yup! :biggrin:
 
Ohh early start I would gather. Anyways, is the quadratic formula the only way it can be done?
 
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.
 
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 :smile:
 
  • #10
Thanks so much tiny-tim, You're a absolute legend
 
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