This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 4

2009 F = Ma, 19

Tags: 2009 , problem 19
A certain football quarterback can throw a football a maximum range of $80$ meters on level ground. What is the highest point reached by the football if thrown this maximum range? Ignore air friction. (A) $\text{10 m}$ (B) $\text{20 m}$ (C) $\text{30 m}$ (D) $\text{40 m}$ (E) $\text{50 m}$

2011 F = Ma, 19

Tags: 2011 , problem 19
After how much time will the particle first return to the origin? (A) $\text{0.785 s}$ (B) $\text{1.26 s}$ (C) $\text{1.57 s}$ (D) $\text{2.00 s}$ (E) $\text{3.14 s}$

2010 F = Ma, 19

Tags: 2010 , problem 19
Consider the following graphs of position [i]vs.[/i] time. [asy] size(500); picture pic; // Rectangle draw(pic,(0,0)--(20,0)--(20,15)--(0,15)--cycle); label(pic,"0",(0,0),S); label(pic,"2",(4,0),S); label(pic,"4",(8,0),S); label(pic,"6",(12,0),S); label(pic,"8",(16,0),S); label(pic,"10",(20,0),S); label(pic,"-15",(0,2),W); label(pic,"-10",(0,4),W); label(pic,"-5",(0,6),W); label(pic,"0",(0,8),W); label(pic,"5",(0,10),W); label(pic,"10",(0,12),W); label(pic,"15",(0,14),W); label(pic,rotate(90)*"x (m)",(-2,7),W); label(pic,"t (s)",(11,-2),S); // Tick Marks draw(pic,(4,0)--(4,0.3)); draw(pic,(8,0)--(8,0.3)); draw(pic,(12,0)--(12,0.3)); draw(pic,(16,0)--(16,0.3)); draw(pic,(20,0)--(20,0.3)); draw(pic,(4,15)--(4,14.7)); draw(pic,(8,15)--(8,14.7)); draw(pic,(12,15)--(12,14.7)); draw(pic,(16,15)--(16,14.7)); draw(pic,(20,15)--(20,14.7)); draw(pic,(0,2)--(0.3,2)); draw(pic,(0,4)--(0.3,4)); draw(pic,(0,6)--(0.3,6)); draw(pic,(0,8)--(0.3,8)); draw(pic,(0,10)--(0.3,10)); draw(pic,(0,12)--(0.3,12)); draw(pic,(0,14)--(0.3,14)); draw(pic,(20,2)--(19.7,2)); draw(pic,(20,4)--(19.7,4)); draw(pic,(20,6)--(19.7,6)); draw(pic,(20,8)--(19.7,8)); draw(pic,(20,10)--(19.7,10)); draw(pic,(20,12)--(19.7,12)); draw(pic,(20,14)--(19.7,14)); // Path add(pic); path A=(0,14)--(20,14); draw(A); label("I.",(8,-4),3*S); path B=(0,6)--(20,6); picture pic2=shift(30*right)*pic; draw(shift(30*right)*B); label("II.",(38,-4),3*S); add(pic2); path C=(0,12)--(20,14); picture pic3=shift(60*right)*pic; draw(shift(60*right)*C); label("III.",(68,-4),3*S); add(pic3); [/asy] Which of the graphs could be the motion of a particle in the given potential? (A) $\text{I}$ (B) $\text{III}$ (C) $\text{I and II}$ (D) $\text{I and III}$ (E) $\text{I, II, and III}$

2008 F = Ma, 19

Tags: 2008 , problem 19
A car has an engine which delivers a constant power. It accelerates from rest at time $t = 0$, and at $t = t_\text{0}$ its acceleration is $a_\text{0}$. What is its acceleration at $t = 2t_\text{0}$? Ignore energy loss due to friction. (a) $\frac{1}{2}a_\text{0}$ (b) $\frac{1}{\sqrt{2}}a_\text{0}$ (c) $a_\text{0}$ (d) $\sqrt{2}a_\text{0}$ (e) $2a_\text{0}$