PROJECTILESSawyer, Will, and Lauren

Quadratic Equations are often used to find maximums and minimums for problems involving projectile motion.

The formula to solve projectiles is…

S(t)=-16t2+vo +so

S(t)-the projectiles height at any time

v ot – the initial velocity

So - initial height projectile is released

t- time in seconds after projectile is released

Example:

Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. Find the highest point reached by the projectile just as it explodes.

Step 1: plug in each part of the equation S(t)=-16t2+80t+0

Step 2: Find the vertex using –b/2a -80/2(-16)

Step 3: Plug the numbers into the equation and solve!

S(t)=-16(-2.5)2+80(-2.5)+0 This highest point is located 100 feet above

the point of release.

On your own…

Question #1 A pistol is accidentally discharged vertically upward at a height of 3 feet above the ground. If the bullet has an initial muzzle velocity of 200 feet per second, what maximum height will it reach before it starts to fall to the ground?

A. 628 feet B. 1,878 feet C. 20.87 feet D. 199.33 feet

Answer to question #1…

Question #2 An over zealous golfer hits a flop shot with a sand wedge to get out of the corner of a sand trip with an initial velocity of 45 feet per second. What is the maximum height that the golf ball will reach?

A. 45 feet B. 13.19 feet C. 36.64 feet D. 95.26 feet

Answer to question #2…

Questions?

Thanks for watching!

Information from http://

algebralab.org/Word/Word.aspx?file=Algebra_MaxMinProjectiles.xml