# How Are Vertical Distances Calculated in Projectile Motion?

• salman213
In summary, the conversation discusses finding the vertical distance traveled by a skier using equations of motion. One equation, s = ut + 1/2at^2, is used to calculate the vertical distance (h) by setting u as the initial vertical velocity and a as the acceleration. The solution also involves differentiating to find the maximum distance. The equation h = y + xtan30 is also used, where h represents the vertical distance and x and y are other variables. The speaker is seeking an explanation for how these equations were derived.
salman213
1. http://img214.imageshack.us/img214/2684/77965080tu2.jpg [/URL]

I get (a) part but for the last part to find the vertical distances can someone explain what is done here. This is the solution

let h be the vertical distance

h = y + xtan30

h= vot tan30 - 1/2gt^2

then they differentiate to find maximum (i get that part). I just don't understand how they came up with those equations for the h distance...

can anyone explain?

Last edited by a moderator:
One of the equations of motion s = ut + 1/2at^2
Where s is distance, u is initial velocity, a is accelaration.
If you only think about the vertical motion of the skier, what is the initial vertical velocity and what is the accelaration.

The equations for the vertical distance (h) are derived using basic kinematic equations. These equations describe the motion of an object under the influence of gravity. In this case, the object is thrown with an initial velocity (vo) at an angle of 30 degrees with respect to the horizontal.

The first equation, h = y + xtan30, is the vertical displacement equation, which relates the vertical distance (h) to the initial height (y) and the horizontal distance (x) traveled. This equation is derived from the fact that the initial velocity can be broken down into its vertical and horizontal components, with the vertical component being vo sin30 and the horizontal component being vo cos30. Using this information, we can find the vertical distance traveled by the object at any given time.

The second equation, h = vot tan30 - 1/2gt^2, is the vertical displacement equation in terms of time. This equation takes into account the acceleration due to gravity (g) and the time (t) that has elapsed since the object was thrown. By differentiating this equation, we can find the maximum value of h, which corresponds to the maximum vertical distance reached by the object.

In summary, these equations are derived from basic kinematic principles and can be used to calculate the vertical distance traveled by an object under the influence of gravity. They are important tools for scientists and engineers in understanding and predicting the motion of objects in the vertical direction.

## 1. What is maximum vertical distance?

Maximum vertical distance refers to the greatest height or distance that an object can reach vertically from its starting point.

## 2. How is maximum vertical distance calculated?

The maximum vertical distance is calculated using the formula: d = v2/2g, where d is the maximum vertical distance, v is the initial vertical velocity, and g is the acceleration due to gravity.

## 3. What factors affect the maximum vertical distance?

The maximum vertical distance is affected by the initial velocity, the angle of launch, and the acceleration due to gravity. Air resistance and other external forces may also play a role.

## 4. What is the significance of maximum vertical distance in physics?

The maximum vertical distance is an important concept in physics as it helps us understand the motion of objects in a vertical direction. It is used to calculate the maximum height reached by projectiles, the trajectory of rockets, and the maximum height of objects thrown in the air.

## 5. How does maximum vertical distance relate to horizontal distance?

The maximum vertical distance and horizontal distance are related through the concept of projectile motion. While the maximum vertical distance is the highest point reached by an object in a vertical direction, the horizontal distance is the distance traveled by the object in a horizontal direction. These two distances are dependent on each other and can be calculated using the same formula for maximum vertical distance.

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