2 A progression: Freefall Review: A ball drops for 3 s. How far does it go? How fast is it going after 3 s?
3 Next… B) Throwing upward: A ball is thrown upward with an initial velocity of 30 m/s. How far does the ball travel? How long before it hits the ground?Divide the motion into two halves- up and downSymmetry:timeup = timedownviup = -vfdowndup = - ddown
4 Next… x y vi = vf = a = d = time = C) Horizontal Projectiles: A balls rolls off a table with a velocity of 10 m/s and lands 30 m away from the table. How long did it take the ball to hit the ground?xyvi =vf =a =d =time =Mythbusters
5 The hardest… D) Projectiles launched at an angle: A ball is launched with a velocity of 100 m/s at 30º above the horizon. How long did it take for the ball to hit the ground? What is the range of the ball? What was the maximum height of the ball?HeightθRange
6 Vi = 100m/sHeightθ = 30ºRangeOur projectile is no longer launched horizontally so it no longer has an viy= 0 m/sThe vi is divided between the x and y directions- we need to do something called “Resolving the x and y components”
13 Now we can take this information and put it into a new form of our table: vi =θ =xyvf =a =d =½ t =t =
14 Revisit our problem: x y vi = 86.6 m/s vf = 86.6 m/s a = 0 m/s d = A ball is launched with a velocity of 100 m/s at 30º above the horizon. How long did it take for the ball to hit the ground? What is the range of the ball? What was the maximum height of the ball?vi = 100 m/sθ = 30ºxyvi = 86.6 m/svf = 86.6 m/sa = 0 m/sd =vi = 50 m/svf = -50 m/sa = -10 m/s2½ t =t =
15 1. Find the maximum height (dy): Vi = 100m/sHeightθ = 30ºRangeHEIGHT WILL LEAD YOU TO TIME
16 2. Finding time: Vtop = Vi = 100m/s θ = 30º Vf = Range Now this becomes like a horizontal projectile problem.Find time.Remember tup = tdown
18 4. Finding components using a ruler and a protractor:
19 Which launch angle gives the greatest range? The cannonball launched at a 45-degree angle had the greatest range. The cannonball launched at a 60-degree angle had the highest peak height before falling. The cannonball launched at the 30-degree angle reached the ground first.
20 Practice Problem:A golf ball is hit with a velocity of 20 m/s at 45 above the horizon. Find the time it takes the golf ball to travel, the range of the golf ball, and the maximum height the golf ball reaches.
21 A player kicks a football from ground level at 27 A player kicks a football from ground level at 27.0 m/s at an angle of 30.0 degrees above the horizontal.Find:its “hang time” (time that the ball is in the air),the distance the ball travels before it hits the ground, andits maximum height.
22 A cannon is fired. The cannonball reaches a maximum height of 22. 5 m A cannon is fired. The cannonball reaches a maximum height of 22.5 m. The range of the cannonball is 89.9 m. At what angle was the cannon fired from?Height = 22.5 mθ = ?Range = 89.9 m