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A golf ball is shot into the air from the ground. If the initial horizontal velocity is 20m/s and the initial vertical velocity is 30m/s, what is the horizontal distance the ball will travel before it hits the ground?

Ans: The golf ball will continue to travel through air until gravity brings it back down to the ground. Under the gravity force, the vertical location of the ball as a function of time is given by the following equation:- $$ z = z_0 + v_{z_0} t - \frac{1}{2} g t^2 $$

The time it takes the golf ball to return the ground is equal to $$ T = \frac{2v_{z_0}}{g} $$

The horizontal distance the ball will travel before it hits the ground can be computed using the following equation:- $$ \Delta x = x-x_0 = v_{x_0} t = 2 v_{x_0} v_{z_0} / g = 122.4\text{ m} $$

The problems are:

1) what is the parameter $v$ represent?

2) In the example above $ \Delta x = x-x_0 = v_{x_0} t = 2 v_{x_0} v_{z_0} / g = 122.4\text{ m} $ What is the actual value in this equation? So that $x=?$ $x_0=?$ $v=30?$ $g=10?$ $z0=?$

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Welcome to Physics.SE, Leo. I've re-formatted you post to take advantage of the MathJax formatting engine which is running on the site. I've also closed it because it appears to violate our site policy on answering specific introductory exercises. If you can reformulate this in terms of the concepts that you are struggling with we can either point you at an existing answered question of re-open this question. –  dmckee Apr 27 '12 at 5:04
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closed as too localized by Manishearth, dmckee Apr 27 '12 at 4:58

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1 Answer

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I think your formatting is messing things up. There are two v's, $v_{x0}$ (i.e horizontal velocity) and $v_{z0}$ (i.e. vertical velocity at $t = 0$). You can get these values right out of the problem statement. Also, $g$ is 9.8m/s. Lastly, $x$ is insignificant; you only need to find $\Delta x$ (even if you were given $x$ it wouldn't effect your final answer).

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Thanks, is the first 2 equation mentioned in my question not relevant to the answer? –  Leo Chan Apr 27 '12 at 4:14
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