Aim: How do we use Newton’s equation of Motion to explain the motion of a free falling projectile?

Free Fall All bodies accelerate downwards at -10m/s2 on earth regardless of mass (in the absence of air resistance). On the moon, the acceleration due to gravity is -1.62 m/s2 . Since there is no air resistance on the moon, a penny and feather will hit the ground at the same time.

Free Fall Problem How long does it take for a basketball to hit the ground when dropped off of the Empire State Building which is 381 meter? 8.82s y=vit + 1/2at2 381=0(t) + ½(9.8)t2 t=8.82 s b) With what speed does the ball hit the ground? 88.2 m/s vf=vi+at vf =0+9.8(10) vf =8.82 m/s

Projectiles Fired Upwards We know three things about projectiles thrown upwards: (Assume no air resistance) The velocity of the projectile at its maximum height is equal to 0.

Projectiles Fired Upwards 2. The time it takes the object to rise is equal to the time it takes the object to fall the same amount of distance.

Projectiles Fired Upwards 3. The velocity with which the projectile is launched upwards will be equal in magnitude to the velocity of the projectile when it hits the ground.

Projectiles Fired Upwards Note: When solving projectile motion problems in which the projectile is fired upwards, it is especially important that we make acceleration vector negative (-9.8) and the initial velocity vector is positive.

Thought Question-Think, Pair, and Share A cream tangerine is thrown vertically upwards and passes through three evenly spaced windows as shown. Rank the windows according to: average speed of tangerine as it passes through each window The time it takes to pass through each window Acceleration while passing each window The change in velocity while passing each window 3>2>1 1>2>3 1=2=3

Problem A With what speed must an object be thrown to reach a height of 91.5 m (equivalent to one football field)? Assume negligible air resistance. How long will object remain in air for?

Problem A Solution

Problem B Gwendolyn throws her crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine how long the crystal vase is in the air if Gwendolyn is 1.2 m tall. Solve for time it takes to reach max height. Solve for distance it rises. Solve for time it takes to fall. Answer: t=5.29 s

Problem B Solution

Problem C A tourist takes a trip in a hot air balloon. The hot air balloon is ascending (moving up) at a velocity of 4 m·s−1. He accidentally drops his camera over the side of the balloon's basket, at a height of 20 m. Calculate the velocity with which the camera hits the ground.

Problem C

Thought Question2- Think, Pair, and Share You throw a ball straight up on the edge of a cliff , and it lands on the ground below the cliff. If you had instead thrown the ball straight down with the same speed, would the ball’s speed just before landing be larger than, smaller than, or the same as previously. SAME SPEED

Problem D-Firing a projectile downwards A mischievous child shoots a pellet out of a BB gun downwards with a velocity of 20 m/s from the top of a building which is 45 m tall. How long does it take the pellet to hit the ground? Vi= -20 m/s Y= -45 m a= -10 m/s^2 Use y=vit +1/2at^2 t= 1.6s

Multiple Choice Question 1 A firework is shot straight up in the air with an initial speed of 50 m/s. What is the maximum height it reaches? 12.5 m 25 m 125 m 250 m 1250 m

Multiple Choice Question 2 On a strange, airless planet, a ball is thrown downward from a height of 17 m. The ball initially travels at 15 m/s. If the ball hits the ground in 1 s, what is this planet’s gravitational acceleration? 2 m/s2 4 m/s2 6 m/s2 8 m/s2 10 m/s2

Multiple Choice Question 3 During a softball game, a batter hits a pop fly. If the ball remains in the air for 6 seconds, how high did it rise? 44 m 36 m 22 m 50 m 74 m