Ahhh! I’m falling Free Fall and Physics

Free Fall 3 IMPORTANT things to remember – We are ignoring fiction. – The object’s mass or shape doesn’t matter – All objects have an acceleration of 9.8 m/s 2

Gravity On Earth we will always use 9.8 m/s 2 – Acceleration due to gravity This is an acceleration which means – The farther the object falls the faster it will be traveling when it hits the ground 0 seconds0 m/s 1 second9.8 m/s 2 seconds19.6 m/s 3 seconds29.4 m/s

Dropping an Object You drop a penny from the top of the Empire State Building (381 meters). How fast is it going when it hits the ground? v i = 0 m/s v f = ? a = 9.8 m/s 2 d = 381 m v f 2 = v i 2 + 2aΔd v f 2 = 0 +2 * 9.8 * 381 final velocity = 86 m/s

Can you kill someone? Nope… – Terminal Velocity is too low We will talk about this later!

Dropping an Object On New Years Eve, they drop an 800 pound peach in Atlanta. Imagine it breaks off from it’s support and falls 150 meters to the ground. How fast would it be going once it hits the ground? v i = 0 m/s v f = ? a = 9.8 m/s 2 d = 150 m v f 2 = 0 +2 * 9.8 * 150 v f 2 = v i 2 + 2aΔd Final velocity = 54 m/s

Your Turn… What will the final velocity of a rock dropped from 4 m be when it hits the ground? 8.9 m/s

New Type of Problem… Your upstairs neighbor drops you an object out of their window above you. There are 2.75 m between the windows. How fast will the object be traveling when it gets to you? How long will it take to reach you? V i = 0 m/s V f = ??? A = 9.8 m/s Δd = 2.75 m Δt = ??? v f 2 = v i 2 + 2aΔd v 2 = * 9.8 * 2.75 Final Velocity = 7.34 m/s a = (v f – v i ) /Δt 9.8 = (7.34 – 0) /Δt Time = 0.75 seconds

Don’t just drop it, throw it… A object is thrown upwards first Remember these things – The initial velocity is no longer 0 – At its highest point, the velocity is 0 – From the highest point down, it is just like a free fall problem – When traveling upwards, gravity’s acceleration is negative

A Picture The velocity from the toss is upwards The acceleration from gravity is downwards At its peak… The vector values for velocity and acceleration are equal. When adding two vectors that are equal and in opposite directions, you get 0! Velocity is 0.

An Example How high will a ball get if you toss it with an initial velocity of 19.6 m/s? V i = 19.6 m/s V f = 0 m/s A = -9.8 m/s Δd = ??? v f 2 = v i 2 + 2aΔd 0 2 = * -9.8 * Δd Distance = 19.6 meters

An Example If it takes 2 seconds for a rock to reach the peak of its throw, what was the initial velocity? How high does it go? V i = ???? V f = 0 m/s A = -9.8 m/s Δd = ??? Δt = 2 seconds d f = d i + v i t f + ½at f 2 d f = 0 + v i 2 + ½*-9.8*2 2 a = (v f – v i ) /Δt -9.8 = (0 – v i ) / m/s = initial velocity d f = *2 + ½*-9.8* m = peak height

An Example A baseball is thrown straight up into the air. The ball reaches its peak 1.5 seconds after it is thrown. How high does it go? V i = ???? V f = 0 m/s A = -9.8 m/s Δd = ??? Δt = 1.5 seconds d f = d i + v i t f + ½at f 2 a = (v f – v i ) /Δt

Your Turn… How high would you have to drop a ball from to have it reach the ground traveling at 35 m/s? (62.5 m) How high would a ball thrown at 20 m/s get before it started falling down again? How long would it take to reach this peak? (20.4 m and 2.05 s)