# Question #8efea

##### 2 Answers

The ball is

#### Explanation:

I'm neglecting air resistance, but can add it in upon request. The body moves in only one dimension, which we shall call

Without air resistance, the only force acting on the body will be gravity - this acts in the negative y direction to provide an unbalanced force which we can use Newton's second law on:

If you are unfamiliar with using calculus to solve problems like this then skip to the blue heading, this is just the derivation of a formula common to introductory dynamics.

Integrating wrt t gives:

The body starts from rest so

Integrate again wrt t:

This is our expression for the displacement from the origin as a function of time. Notice it's very similar to the common expression

which describes displacement under constant acceleration. This is because it is the exact same derivation, we have just accounted for the fact that initial speed is zero while doing it.

Anyway, onto solving the problem:

If it takes T seconds to reach the ground,

Note that we discard the negative solution from the square root because negative time doesn't really make sense.

The body is at

#### Explanation:

Kinematic equation for the body dropped from a height

where

Inserting given values we get

Similarly height

Dividing (2) by (1) we get