PedGames Project Curriculum Document
Platform Game Math Worksheet 2
Tags: Player Movement, Speed, Gravity, Equations of Motions
Math Standards: California Standards - Algebra and Functions (AF), Mathematical Reasoning
(MR), Number Sense(NS),
Common Core Standards - High School Algebra – Creating Equations, Reasoning with
Equations & Inequalities
Definitions:
Following are the two formulas required for solving the worksheet.
1) v = u + at
2) v2 = u2 + 2as
where the symbols are as follows:
v = final velocity
u = initial velocity
s = displacement (distance between initial and final position)
a = acceleration
t = time taken to move from initial to final state.
In Game Maker,
Velocity (u & v) means how many pixels an object moves per step (pixels / step)
Displacement(s) is the no.of pixels.
Acceleration(a) = pixels / step2
Time (t) = no. of steps
Game Maker is set to have 30 steps per second by default.
Hence to calculate time in sec, divide time steps / 30 steps per second = time (sec).
PedGames Project Curriculum Document
Problem:
1) Fill the table below with jump times observed from platformtest2.gm81, given gravity
values as follows:
(Note: To jump, press UP arrow key once and release)
Gravity
2.0
Jump Time
PedGames Project Curriculum Document
1.3
0.8
0.7
0.2
Eg: 2) Using the formula v = u + at, calculate the jump time of the ball when gravity is 1.0 pixels
/ step2, given initial velocity = 12 pixels / step. AF 4.2, MR 1.1, 1.3, A.CED.1, A-REI.3
Soln:
Given:
Initial Velocity u = 12 pixels / step
Final Velocity v = 0 (At maximum height, the ball stops, hence v = 0)
Acceleration (gravity) a = -1.0 pixels / step2 (gravity acts downwards whereas ball is thrown
upwards hence negative acceleration).
Using the equation (v = u + at)
We have,
0 = 12 + (-1.0) x t
t = 12 steps.
Time in sec = 12 / 30 = 0.4 secs.
This is the time required for the ball to reach max height.
Now total jump time = 2 x time required for the ball to reach max height.
= 2 x 0.4
= 0.8 secs.
Ans 2: Jump time of the ball = 0.8 secs.
Q2) Calculate the jump time of the ball when gravity is 0.2 pixels / step2, given initial velocity =
12 pixels / step. AF 4.2, MR 1.1, 1.3, A.CED.1, A-REI.3
PedGames Project Curriculum Document
Eg 3) Using the formula v = u + at, calculate the gravity of the world that needs to be set, when
the jump time of the ball = 0.5 sec, given initial velocity = 12 pixels / step. AF 4.1, MR 1.1, 1.3,
A.CED.1, A-REI.3
Soln:
Given:
Initial velocity u = 12 pixels / step.
Jump Time = 0.5 secs.
Final velocity v = 0 ( At maximum height the ball stops, hence v = 0)
Calculate : a (gravity) = ?
Since total jump time = 0.5 secs, time required to achieve max height = jump time / 2.
Therefore t = 0.5 / 2 = 0.25 secs.
Converting into t (steps) = 0.25 sec x 30 steps / sec = 7.5 steps.
Using the equation ( v = u + at)
0 = 12 + a x 7.5
a = -12 / 7.5
a = -1.6 pixels / step2.
PedGames Project Curriculum Document
Hence gravity = 1.6 pixels / step2. (Acceleration due to gravity is negative since it acts in
opposite direction to the ball thrown upwards.).
Ans: Gravity = 1.6 pixels/step2.
Q3) Using the formula v = u + at, calculate the gravity of the world when the jump time of the
ball = 1.6 sec, given initial velocity = 12 pixels / step. AF 4.1, MR 1.1, 1.3, A.CED.1, A-REI.3
4) Fill the table below with the height attained by the ball when the gravity values are as follows:
(Use platformTest2.gm81 to fill the table.)
Gravity
2.0
1.5
0.9
Height Attained by the Ball
PedGames Project Curriculum Document
0.7
0.4
Eg 5) Using the formula, v2 = u2 + 2as, calculate the height attained by the ball when gravity is
set to 0.8 pixels / step2 and initial velocity = 12 pixels / step. AF 4.2, MR 1.1, 1.3, Algebra I 23.0,
NS 2.4, A-CED.1, A-REI.3
Soln:
Given:
Initial Velocity u = 12 pixels / step.
Final Velocity v = 0.
a = -0.8 pixels / step2.
Using the equation v2 = u2 + 2as,
0 = 122 – 2 x 0.8 x s
-144 = -1.6s
s = 144 / 1.6
s = 90 pixels.
Ans 5: Height attained by the ball = 90 pixels.
Q5) Using the formula v2 = u2 + 2as, calculate the height attained by the ball when gravity is set
to 0.5 pixels/ step2 and initial velocity = 12 pixels/step. AF 4.2, MR 1.1, 1.3, Algebra I 23.0, NS
2.4, A-CED.1, A-REI.3
PedGames Project Curriculum Document
Eg 6) Using the formula v2 = u2 + 2as, calculate the gravity of world when the ball achieves a
max height of 72 pixels given that it is thrown with a velocity of 12 pixels/step - AF 4.2, MR 1.1,
1.3, Algebra I 23.0, NS 2.4, A-CED.1, A-REI.3
Soln:
Given:
Initial Velocity u = 12 pixels/step,
Final Velocity v = 0.
s = 72 pixels.
Find : a =?
Using the equation, v2 = u2 + 2as,
0 = 122 + 2 x a x 72
-144 = 144a
a = -1 pixel/step2.
Hence gravity = 1 pixels/step2.
Ans 6: Gravity of the world = 1 pixels/step2.
Q6) Using the formula v2=u2+2as, calculate the gravity of the world when the ball achieves a
max height of 180 pixels given that it is thrown with a velocity of 12 pixels /step. AF 4.2, MR 1.1,
1.3, Algebra I 23.0, NS 2.4, A-CED.1, A-REI.3