Acceleration due to gravity question?

[jbgibson]

If I know the acceleration of gravity (9.81m/s^2), and I'm given an initial velocity in the positive x direction, how would I go about figuring how far will an object fall in a given time?

I think this a 2-dimension projectile, but I don't see how to solve. If y=yo+vot-1/2gt^2, then y=-1/2gt^2. Any help is greatly appreciated!

 

[Monocles]

The velocity in the x direction won't affect the velocity in the y direction. All you need is that first equation.

 

[baba89]

I can provide some guidance on how to approach this problem. First, it is important to note that the equations for projectile motion are derived from the laws of motion and apply to objects moving in two dimensions due to gravity. In this case, we are considering the vertical motion of an object, which is affected by the acceleration due to gravity (g) and the initial velocity in the positive x direction (vo).

To solve for the distance an object will fall in a given time, we can use the equation y = yo + vot - 1/2gt^2, as you have correctly identified. This equation represents the displacement (y) of the object from its initial position (yo) at a given time (t), taking into account the initial velocity (vo) and the acceleration due to gravity (g).

To find the distance the object will fall, we can rearrange the equation to solve for y as follows: y = yo + vot - 1/2gt^2. We can then substitute the known values for yo, vo, and g, and the given time (t) to calculate the displacement (y).

It is also important to keep in mind that this equation assumes that the object is falling in a vacuum, without any air resistance. In reality, air resistance will affect the motion of the object and may result in a slightly different distance fallen.

I hope this explanation helps you solve the problem. Remember to always carefully define and consider all the variables involved in a problem, and use appropriate equations to solve it accurately.