Freefall & Vertical Motion Aim: How does an object’s motion vary when moving in a vertical direction?

They both hit at the same time! “SAME HEIGHT = SAME TIME!!!” Which Will Land First? An astronaut on the moon drops a hammer and a feather from the same height, at the same time. Which one will land first? They both hit at the same time! “SAME HEIGHT = SAME TIME!!!”

Gravity Earth: g = 9.81m/s2 Objects fall due to the pull of GRAVITY Gravity causes things to ACCELERATE toward the center of the object; in this case the planet Earth We use lowercase “g” to represent the ACCELERATION DUE TO GRAVITY Earth: g = 9.81m/s2 When dealing with vertical motion, ALWAYS ASSUME ITS ON EARTH, UNLESS OTHERWISE SPECIFIED! When an object is either “Dropped” or “Falls from rest”, assume that vi = 0m/s If all your given values (displacement/velocity/acceleration) go in the SAME DIRECTION, you may make them all POSITIVE VALUES even though they are going down

Example #1 A baseball is dropped from the top of a building. Calculate how fast the baseball travels after (a) 1 second, (b) 2 seconds and (c) 3 seconds a) b) c)

Example #2 A baseball is dropped from the top of a building. Calculate how far the baseball travels after (a) 1 second, (b) 2 seconds and (c) 3 seconds a) b) c)

Example #3 The baseball is now thrown straight downward at a speed of 10m/s and takes 5 seconds to hit the ground. (a) How tall is the building and (b) how fast does the ball travel as it hits the ground? a) b)

Initial Vertical Upwards Velocity vtop = 0m/s When an object is initially going upward, make sure your values match their direction (Up is positive and down is negative) When the object moves upwards, it slows down due to the pull of gravity and MOMENTARILY STOPS at the pinnacle “Maximum Height”  vtop = 0m/s The time it takes to reach the maximum height is equal to the time it takes to come back down Total Time in Air = 2×tup Since gravity is ALWAYS pulling the object down, it will speed up as it falls vup has the same magnitude as vdown but OPPOSITE DIRECTIONS tup = tdown g = -9.81m/s2 vup = (+) vdown = (-)

Example #4 vtop = 0m/s A toy rocket has a launch speed of 50m/s. (a) How high does the toy rocket reach? (b) How long does it take to land? (a) (b) vup = 50m/s

SUMMARY What is the acceleration due to gravity on the Earth? What is the initial velocity of an object that… Is dropped? Initially goes straight downward? Initially goes straight upward? At maximum height, what is the object’s… Velocity? Acceleration?