Write a C program to simulate the behavior of a falling object.

Your program should use Euler$$s method to numerically solve the differential equations describing the

motion of a falling object. In Euler$$s method, the state of the object at some small future time, is

calculated using the values at the present time. This small future time step is typically called delta time,

or dt$.$ Thus, the position $($p$)$ and speed $($s$)$ of the object in the next timestep t $+$ dt is written as a simple

function of the position and speed at the current timestep t $($g is the acceleration due to gravity$)$:

s$($t $+$ dt$)=$ s$($t$)+$ g $*$ dt

p$($t $+$ dt$)=$ p$($t$)+$ s$($t $+$ dt$)*$ dt

Your program should determine the amount of time required for the object to fall to the ground and the

impact speed of the object when it reaches the ground.

Use the following algorithm to determine the fall time and impact speed of the object:

$1.$ Initialize the speed of the object to zero.

$2.$ Initialize the position of the object to the initial height specified by the user.

$3.$ Determine the new speed of the object using the formula given above.

$4.$ Determine the new position of the object using the formula:

p$($t $+$ dt$)=$ p$($t$)-$ s$($t $+$ dt$)*$ dt

$5.$ Repeat until the object reaches the ground $($i$.$e$.$ the position is less than or equal to zero$).$

ECE $240$ C Programming for Engineers $4$ of $6$ Dr$.$ Craig Lorie

Homework Assignment #$5$ Spring $2024$

The value of the time step $($dt$)$ that you use in the simulation is important. If the time step is too large,

the results will not be accurate. If the time step is too small, the program run time will be too long.

Your program must do the following:

$1.$ Prompt the user to enter the initial height of the object in either feet or meters.

$2.$ Read the input from the keyboard.

$3.$ Determine the time for the object to fall to the ground $($in seconds$).$

$4.$ Determine the impact speed of the object when it reaches the ground.

$$ Calculate the impact speed in ft$/$sec and mph if the initial height was specified in feet.

$$ Calculate the impact speed in m$/$sec and kph if the initial height was specified in meters.

$5.$ Determine the proper value for the time step $($dt$).$

$$ The value of the time step should be as large as possible $($to minimize run time$).$

$$ But should also result in an answer that is accurate to five decimal places to the right of

the decimal point.

$$ That is$,$ decreasing the time step further will not improve the accuracy of the result.

$$ You should submit your program using this value for the time step.

$6.$ Output the fall time and impact speed of the object.