** Using WeBWorK **

# DESCRIPTION

#

# WeBWorK problem written by Justin Heckman

# Council Bluffs Community Schools

# ENDDESCRIPTION

## DBsubject('')

## DBchapter('')

## DBsection('')

## KEYWORDS('')

## TitleText1('')

## EditionText1('')

## AuthorText1('')

## Section1('')

## Problem1('')

## Author('Justin Heckman')

## Institution('Council Bluffs Community School District')

DOCUMENT();

loadMacros("PGbasicmacros.pl",

"PGstandard.pl",

"PGcourse.pl",

"MathObjects.pl",

"PGauxiliaryFunctions.pl",

"PGchoicemacros.pl",

"PGanswermacros.pl",,

"answerHints.pl",

"scaffold.pl",

"parserNumberWithUnits.pl",

"parserFormulaWithUnits.pl",

"PGML.pl",

"parserPopUp.pl"

);

######################################################################################

Context("Numeric");

$xh= random(10, 30, 2);

$vb= random(5, 15 , 1);

$vobu= NumberWithUnits("0 m/s");

$g=(9.81);

$ag= NumberWithUnits("9.81 m/s^2");

$xhu= NumberWithUnits("$xh m");

$t= (sqrt(2*$xh/$g));

$tu= NumberWithUnits("$t s");

$xb= ($vb*$t);

$xbu= NumberWithUnits("$xb m");

$xhgg= random(150, 200, 2);

$vC= random(20, 30, 1);

$tbgg= (sqrt(2*$xhgg/$g));

$xC= ($vC*$tbgg);

$ns= ($xC/4);

$nsu= NumberWithUnits("$ns m");

$popup = PopUp(

["?","a","b","c"],

"c",);

###################################################

TEXT(beginproblem());

###################################################

BEGIN_PGML

The subject of the 16 bit game Water Balloon Drop was to drop water

balloons from the top of buildings on unsuspecting bystanders. While the

game was rather lame a lacked dimension it does make for a good physics

problem. By examining the height of the characters in the game in comparison

to the height that the balloons were dropped,it can be determined that the

balloons are being dropped from a height of [$xh] m . Considering that

cyclists are worth more points and that they travel at a rate of [$vb] m/s on average

we can use the following to determine how much ahead of a cyclist a balloon

must be dropped to strike a cyclist.

a.) To find the answer to the posed question we will need to determine the the time it take for

the balloon to fall to the ground. To do so we will need to fill out a [:vvaxt:]. By examining the

scenario we can determine the initial velocity of the water balloon, what is it?

[_____]{$vobu}.

b.) Since the building is on earth we can also determine the rate at which the balloon speeds

up as it fell, a value we refer to as the acceleration due to gravity. What is the

acceleration?

[_____]{-$ag}.

c.) Finally, we know the distance (x) that the balloon will fall, enter it now!

[_____]{$xhu}.

d.) Now that we have 3 pieces of information in our vvaxt we can now determine the

remaining pieces. Since we really want to know how far the

bike will travel in the time it takes for the balloon to fall what

we need to calculate is the time (t) that it takes the balloon to

fall to the ground. Which formula will you use to solve for

time?

A.) [: V_f=v_o+at :]

B.) [:v_f^2=v_o^2+2ax:]

C.) [:x=v_o*t = (1/2*a*t^2):]

[@ $popup->menu() @]*

e.) How long will it take the balloon to fall to the ground?

[_____]{$tu}.

f.) Considering that the cyclist travels at 6 m/s how far in front of the moving cyclist should the

balloon be dropped?

[_____]{$xbu}.

g.) The subject of a totally different but similar

game is to drop water balloons from the top of the

golden gate bridge tower on top of passing cars.

The towers have a height of [$xhgg] meters, according

to Google, and that cars drive an average of [$vC] m/s

across the bridge. In this game we will assume that

the beginning of each white stripe is 4 m from the

beginning of the next (2m stripe and 2m gap). If this

is game how many white stripes away from the edge

of the beam should a car be when the balloon is released in order to strike a car traveling at

average speed?

[_____]{$nsu}.

END_PGML

install_problem_grader(~~&std_problem_grader);

$showPartialCorrectAnswers = 0;

ANS( $popup->cmp() );

####################################################

ENDDOCUMENT();