How Can I Solve 2D Kinematics Problems Using the Quadratic Formula?

[dolpho]

Homework Statement

A projectile is shot from the edge of a vertical cliff 60.0meters above the ocean. It has a speed of 100m/s and is fired at an angle of 35 degrees above horizontal. How far from the foot of the vertical cliff does the projectile land.

Homework Equations

Yf= Yinitial + ViT + 1/2 aT^2

The Attempt at a Solution

Ok so I can solve this problem but what really confuses me is why I can't solve for T using Y= Yinitial + ViT + 1/2 aT^2. I think they give us all the variables to solve it this way.

Yf = 0, Y initial = 60, Vi = 57.4, a = -9.8m/s^2

So I set it up like, 0=60+57.4T-4.9t^2
From there I factor out a T, -60=t(57.4- 4.9t)
t= -117, -/ 4.9= t
=23.9 seconds.

(I assume we lose possible solutions if I factor out the T, so instead I have to use the quadratic formula? Not sure though)

And just a random question, Does anyone know where they gave a bunch of 2d kinematic examples and ones regarding force? I've been looking all day but can't really find a bunch of examples for practice. Thanks guys!

 

[tiny-tim]

hi dolpho!

(try using the X² and X₂ buttons just above the Reply box)

Homework Statement

So I set it up like, 0=60+57.4T-4.9t^2
From there I factor out a T, -60=t(57.4- 4.9t)
t= -117, -/ 4.9= t
=23.9 seconds.

sorry, not following that

use the usual quadratic equation formula (the negative result is the time t at which it would have had to be thrown from the foot of the cliff to reach the top at 35° at t = 0)

 

[dolpho]

Oh woops, sorry!

-60 = t (57.4 - 4.9t)
one of the t's goes away t=0
-117.4 = -4.9t

Which is like 23 something which isn't the right one! :| Argggg guess I'll have to use the quadratic formula...I hate that thing

 

[tiny-tim]

-60 = t (57.4 - 4.9t)
one of the t's goes away t=0
-117.4 = -4.9t

no, you can't do that, t = 0 isn't a solution, is it?

 

[dolpho]

no, you can't do that, t = 0 isn't a solution, is it?

No :( But it works sometimes! when I have like... 0 = 4t + 12t² and I factor out a t.

Then it's t=0, and -4 = 12t

-4/12 = -.33 and that comes out to be the right answer on the homework or something. It's hard to find an example but it's messing with my mind! I'll try to look for one. :) Ty for help :D

My calculus class is solving acceleration and velocity problems by taking derivatives and factoring. I think that's why I'm so confused.

 

[tiny-tim]

No :( But it works sometimes! when I have like... 0 = 4t + 12t² and I factor out a t.

Then it's t=0, and -4 = 12t

yes, you certainly can factor out t if the LHS is 0, because 0/t is still 0

but if the LHS is 60, you get 60/t = 57.4 - 4.9t ​