Solve Kinematics Problem: y = y0 + Vot + 1/2gt²

[James_22]

Homework Statement

Homework Equations

y = y0 + Vot + 1/2gt²

The Attempt at a Solution

We have to know when yball = y rock
for the ball : t = t-1 because it's throwed 1 sec later the rock.
we have to fine when yball = yrock :

12.t - 0.5*9.8*t² = 18*(t-1) - 0.5*9.81*(t-1)²..I find the answer with this equation.. t = 1.45 y=7.43
but my first equation was : -12.t - 0.5*9.8*t² = 18*(t-1) - 0.5*9.81*(t-1)²
I put the sign (-) before 12t because I thought when acceleration and velocity have the same direction they have the same sign but when I do that, I don't find the good answer. If someone can explain me that..
Thank you

 

[gneill]

The signs associated with values depends upon your choice of coordinate system.

Generally you choose your coordinate system before assigning signs to things accordingly. In this case if you chose your coordinates so that upwards is positive, then an upward velocity is positive. Gravitational acceleration is always downwards, so that's why it gets the negative sign.

 

[SteamKing]

Homework Statement

View attachment 95959

Homework Equations

y = y0 + Vot + 1/2gt²

The Attempt at a Solution

We have to know when yball = y rock
for the ball : t = t-1 because it's throwed 1 sec later the rock.
we have to fine when yball = yrock :

12.t - 0.5*9.8*t² = 18*(t-1) - 0.5*9.81*(t-1)²..I find the answer with this equation.. t = 1.45 y=7.43
but my first equation was : -12.t - 0.5*9.8*t² = 18*(t-1) - 0.5*9.81*(t-1)²
I put the sign (-) before 12t because I thought when acceleration and velocity have the same direction they have the same sign but when I do that, I don't find the good answer. If someone can explain me that..
Thank you

When you throw something upward, its initial velocity is going to be reduced by the gravitational attraction of the Earth on it, so the velocity term and the acceleration term will have opposite signs. After the object has reached its highest point above the ground and starts to fall back to earth, its velocity is increased by the same gravitational attraction, so the velocity term and the acceleration term will have the same sign.

 

[haruspex]

but my first equation was : -12.t - 0.5*9.8*t² = 18*(t-1) - 0.5*9.81*(t-1)²
I put the sign (-) before 12t because I thought when acceleration and velocity have the same direction they have the same sign

Ok, but what made you think they have the same direction here?