Vertical Motion We have investigated horizontal motion NOW

Vertical Motion

We have investigated horizontal motion. NOW, we will study vertical motion.

Objects fall because of gravity. If gravity is the only force acting on a falling object, we say it is in free fall.

Describe the speed of an object that is dropped. The speed increases. Describe the speed of an object projected upward into the air. The speed decreases until it reaches zero at the apogee then the object’s speed increases as it moves toward the earth’s surface.

In real life, air resistance affects how objects move. But air resistance complicates matters, so we will neglect it, for now.

On the earth’s surface the acceleration due to gravity is 10 m/s 2. (The real value is 9. 8. m/s 2, but we’ll use “ 10”to make it easier. )

Acceleration due to gravity is given the symbol “g”. g = 10 2 m/s

Since acceleration due to gravity is 10 m/s/s, objects gain or lose speed at a rate of 10 m/s each second when projected into the air or dropped.

A shoe is projected into the air. Identify how long the object is in the air and the speed and acceleration at each point. t= a= a= v= t= a= v= a= a= v= t= t= v= a= v = 40 m/s t=0 s t= v= a=

A shoe is projected into the air. Identify how long the object is in the air and the speed and acceleration at each point. t= 4 s v= 0 m/s a = 10 m/s 2 a= 10 m/s 2 v = 10 m/s t = 3 s t= 5 s v= 10 m/s a = 10 m/s 2 a= 10 m/s 2 v = 20 m/s t = 2 s t= 6 s v= 20 m/s a = 10 m/s 2 a= 10 m/s 2 v = 30 m/s t = 1 s t= 7 s v= 30 m/s a = 10 m/s 2 a= 10 m/s 2 v = 40 m/s t = 0 s t= 8 s v= 40 m/s a = 10 m/s 2

Notice that at equal heights, there is equal speed.

The speed of an object dropped from rest can be found by: vf = at = gt = (10 m/s 2) t Where vf is the final speed of the object at the end of time, t. vf = 10 t

vf = 10 t What is the speed of an object after falling from rest for: 1 s v = 10(1) = 10 m/s 2 s v = 10(2) = 20 m/s 3 s v = 10(3) = 30 m/s 5 s v = 10(5) = 50 m/s 10 s v = 10(10) = 100 m/s

The distance an object falls when dropped from rest can be found by: d = ½ at 2 = ½ gt 2 = ½ (10 m/s 2) t 2 = (5 m/s 2) t 2 Where d is the distance an object falls in time, t. d= 2 5 t

d= 2 5 t If dropped from rest, how far would a ball fall in: 1 s d = 5(12) = 5 m 2 s d = 5(22) = 20 m 3 s d = 5(32) = 45 m 5 s d = 5(52) = 125 m 10 s d = 5(102) = 500 m

Fred drops a bowling ball from the top of this monument. If it drops for 12 s, how fast is it going just before it hits the ground? What is the height of the monument? vf = 10 t = 10(12) = 120 m/s d = 5 t 2 = 5(122) = 720 m

The world record high jumper is Javier Sotomayor of Cuba, born in 1967. He reached a height of 2. 45 m. Find Javier ‘s hang time.

The world record high jumper is Javier Sotomayor of Cuba, born in 1967. He reached a height of 2. 45 m. Find Javier ‘s hang time. d = 5 t 2 2. 45 = 5 t 2 . 49 = t 2 Javier drops for. 7 sec, so he is in the air: . 7 sec = t . 7 sec x 2 = 1. 4 sec

FIELD TRIP !!!!!!! Given a ball and a stopwatch, let’s find the height of the flag pole.

Fred is being chased by a sharptooth. He remembers seeing “The Land Before Time”. He decides to drop a boulder to stop the dinosaur. Fill in the chart: height 125 m a distance fallen above ground t v 0 s 0 m/s 10 m/s 2 0 m 125 m 1 s 10 m/s 2 5 m 120 m 2 s 20 m/s 10 m/s 2 20 m 105 m 3 s 30 m/s 10 m/s 2 45 m 80 m 4 s 40 m/s 10 m/s 2 80 m 45 m 5 s 50 m/s 10 m/s 2 125 m 0 m

What vertical speed must a ball have to rise to a height if 15 m?

What vertical speed must a ball have to rise to a height if 15 m? The speed at the start = speed at the end. The speed at the end is determined by how long it takes the ball to fall 15 m. d = 5 t 2 15 = 5 t 2 3 = t 2 1. 73 sec = t vf = 10(1. 73) vf = 17. 3 m/s vi = 17. 3 m/s