February 8, Week 4 Today: Chapter 3, Projectile Motion Homework #1 now in boxes. No New homework assignment this week. Homework Solutions posted Thursday morning. Chapter 2 practice problems on Mastering Physics. Exam #1 Friday, February 10. Practice Exam available on website. Review Session, Thursday, 7:30 PM in room 114 of Regener Hall. Projectile Motion p. 1/9
Projectile Motion Projectile Motion is one example of two-dimensional motion with a constant acceleration. Projectile Motion p. 2/9
Projectile Motion Projectile Motion is one example of two-dimensional motion with a constant acceleration. Projectile - Any object that is launched into motion and then acted on by gravity only. Projectile Motion p. 2/9
Projectile Motion Projectile Motion is one example of two-dimensional motion with a constant acceleration. Projectile - Any object that is launched into motion and then acted on by gravity only. Ignore air resistance again. Projectile Motion p. 2/9
Projectile Equations General Equations v x = v o,x +a x t v y = v o,y +a y t x = x o +v o,x t+ 1 2 a xt 2 y = y o +v o,y t+ 1 2 a yt 2 Projectile Motion p. 3/9
Projectile Equations General Equations v x = v o,x +a x t v y = v o,y +a y t x = x o +v o,x t+ 1 2 a xt 2 y = y o +v o,y t+ 1 2 a yt 2 Gravity pulls straight down, so it causes acceleration in the y-direction only. Projectile Motion p. 3/9
Projectile Equations General Equations v x = v o,x +a x t v y = v o,y +a y t x = x o +v o,x t+ 1 2 a xt 2 y = y o +v o,y t+ 1 2 a yt 2 Gravity pulls straight down, so it causes acceleration in the y-direction only. a x = 0,a y = g (Down is negative ) Projectile Motion p. 3/9
Projectile Equations II Substituting a x = 0, a y = g into our general equations, gives us the equations of motion for a projectile. General Equations v x = v o,x +a x t v y = v o,y +a y t x = x o +v o,x t+ 1 2 a xt 2 y = y o +v o,y t+ 1 2 a yt 2 Projectile Motion p. 4/9
Projectile Equations II Substituting a x = 0, a y = g into our general equations, gives us the equations of motion for a projectile. General Equations v x = v o,x v y = v o,y +a y t x = x o +v o,x t+ 1 2 a xt 2 y = y o +v o,y t+ 1 2 a yt 2 Projectile Motion p. 4/9
Projectile Equations II Substituting a x = 0, a y = g into our general equations, gives us the equations of motion for a projectile. General Equations v x = v o,x v y = v o,y +a y t x = x o +v o,x t y = y o +v o,y t+ 1 2 a yt 2 Projectile Motion p. 4/9
Projectile Equations II Substituting a x = 0, a y = g into our general equations, gives us the equations of motion for a projectile. General Equations v x = v o,x v y = v o,y gt x = x o +v o,x t y = y o +v o,y t+ 1 2 a yt 2 Projectile Motion p. 4/9
Projectile Equations II Substituting a x = 0, a y = g into our general equations, gives us the equations of motion for a projectile. Projectile Equations v x = v o,x v y = v o,y +gt x = x o +v o,x t y = y o +v o,y t 1 2 gt2 Projectile Motion p. 4/9
Horizontal Launch The equations of motion simplify even further in the case the projectile is launched horizontally. y vo x Projectile Motion p. 5/9
Horizontal Launch The equations of motion simplify even further in the case the projectile is launched horizontally. y vo x vo has no vertical component v o,x = v o,v o,y = 0 Projectile Motion p. 5/9
Horizontal Launch The equations of motion simplify even further in the case the projectile is launched horizontally. y vo x vo has no vertical component v o,x = v o,v o,y = 0 Projectile Equations v x = v o,x v y = v o,y gt x = x o +v o,x t y = y o +v o,y t 2 1gt2 Projectile Motion p. 5/9
Horizontal Launch The equations of motion simplify even further in the case the projectile is launched horizontally. y vo x vo has no vertical component v o,x = v o,v o,y = 0 Projectile Equations v x = v o v y = v o,y gt x = x o +v o,x t y = y o +v o,y t 2 1gt2 Projectile Motion p. 5/9
Horizontal Launch The equations of motion simplify even further in the case the projectile is launched horizontally. y vo x vo has no vertical component v o,x = v o,v o,y = 0 Projectile Equations v x = v o v y = v o,y gt x = x o +v o t y = y o +v o,y t 1 2 gt2 Projectile Motion p. 5/9
Horizontal Launch The equations of motion simplify even further in the case the projectile is launched horizontally. y vo x vo has no vertical component v o,x = v o,v o,y = 0 Projectile Equations v x = v o v y = gt x = x o +v o t y = y o +v o,y t 1 2 gt2 Projectile Motion p. 5/9
Horizontal Launch The equations of motion simplify even further in the case the projectile is launched horizontally. y vo x vo has no vertical component v o,x = v o,v o,y = 0 Projectile Equations v x = v o v y = gt x = x o +v o t y = y o 1 2 gt2 Projectile Motion p. 5/9
General Launch Angle y α vo x v o = launch speed α = launch angle Projectile Motion p. 6/9
General Launch Angle y α vo x v o = launch speed α = launch angle No shortcuts here! v o,x = v o cosα, v o,y = v o sinα Projectile Motion p. 6/9
General Launch Equations Projectile Equations v x = v o,x v y = v o,y gt x = x o +v o,x t y = y o +v o,y t 1 2 gt2 v o,x = v o cosα v o,y = v o sinα Projectile Motion p. 7/9