Finding the Velocity of a Cart at its Highest Point

[2slowtogofast]

A cart is propelled over an xy plane with acceleration components ax=4.0m/s^2 and ay= -2.0m/s^2 . Its initial velocity has components Vix=8.0m/s and Viy12 m/s. In unit-vector notation, what is the velocity of the cart when it reaches its greatest y coordinate?



im confused on how to get this going. Since the cart is at its highest point the velocity in the y direction is 0. could some one help me with the next step of this thanks

 

[<---]

So you know that,

$$v_y = f(t) = 0$$

at your highest point.
Well you should also know that $$v_x = f(t)$$ where "t" is the same as the "t" for your y position.

Does that help?

 

[2slowtogofast]

no I am still confused

 

[<---]

Ok, you already have the necessary x and y components, so you can treat each one like a one dimensional problem right?
Do you know the equations for position/velocity/acceleration as functions of time? If not check out the formulas in in the sticky thread and go back over your textbook.
Once you have the equation for velocity as a function of time, you only need to solve for time using your knowledge that the y-component velocity equals zero at the needed time. with this value of t you can calculate the x-component velocity.

 

[2slowtogofast]

thanks

 

[2slowtogofast]

i think i have the answer i was just wondering if someone could tell me if i am right.

I used the eqn V = Vi + at
because the y velocity at the highest point is zero i used that for V
-12 for Vi
-2.0 for a

and got time = 6 seconds.

then i used the same eqn with this time = to 6 seconds and used 4.0 for a and 8.0 for Vi. All the horizontal inforamtion. I got 32 m/s for an answer.

so in unit vector notation the answer would be 32i +0j = V

 

[ravsdanteml]

Please, would someone explain me how do you know that at its highest point the velocity of the cart is 0 in its y coordinate. Well, i am trying to figure out how do the problem, as it seems easy, but it really isn't. I would really appreciate someone explaining it. Please reply.