Objectives Students should be able to add, subtract, and resolve displacement and velocity vectors so they can: Determine the components of a vector along two specified, mutually perpendicular axes. Determine the net displacement of a particle of the location of a particle relative to another. Determine the change in velocity of a particle or the velocity of one particle relative to another. Students should understand the motion of projectiles in a uniform gravitational field, so they can: Write down expressions for the horizontal and vertical components of velocity and position as functions of time, and sketch or identify graphs of these components. Use these expressions in analyzing the motion of a projectile that is projected with an arbitrary initial velocity.
Bell Ringer A small error in the beginning is a great one in the end. The Philosopher (Aristotle) A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land? A. Forward of the center of the car B. At the center of the car C. Backward of the center of the car correct x- direction: Ball and car start with same position and velocity, a=0, so always have same position
Bell Ringer I shoot a 1000 kg buick from a cannon at an angle of 77 degrees from the horizontal and an initial velocity of 19 m/s. The buick travels downrange 16.4 m, reaches a height of 17.55 m and is in the air for 3.5 s. Question: What happens next? Answer: Score!!!!! http://phet.colorado.edu/en/simulation/projectile-motion http://www.mhhe.com/physsci/physical/giambattista/proj/projectile.html http://www.fearofphysics.com/proj/proj.html
Monkey Troubles You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting? A Right at the monkey B Below the monkey C Above the monkey 30 39
Shooting the Monkey... Dart x = v 0 t y = - 1 / 2 g t 2 Monkey x = x 0 y = - 1 / 2 g t 2
Shooting the Monkey... Still works even if you shoot upwards! y = y 0-1 / 2 g t 2 y = v 0y t - 1 / 2 g t 2 Dart hits the monkey
Shoot The Monkey http://jersey.uoregon.edu/vlab/newcannon /NewCannon_plugin.html
More complex projectile motion problems require you separate a resultant velocity vector into its components using sin, cos, tan A stone is thrown at 25 m/s at a 40º angle with the horizon. Start with the finding the v x and v oy Then solve the problem like we have v oy
Field Goal Example Our field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal? y x 3 m Y-direction v y0 = v sin(30) = 15 m/s y = y 0 + v y t + ½ a t 2 D Y-direction v x0 = v cos(30) = 26 m/s D = x 0 + v x0 t + ½ a t 2 3m = 0m + 15m/s t ½ (9.8 m/s 2 ) t 2 = 0m + (26m/s)(2.8 s) + 0 m/s 2 (2.8 s ) 2 t = 2.8 s or t = 0.22 s. = 72.8 m Our kicker can kick a 70 yard Field Goal!!!!!
A 70 yard field goal Record is apparently 68 yards without a tee.
The Lab g: the gravitational acceleration usually taken to be 9.81 m/s 2 θ: the angle at which the projectile is launched v: the velocity at which the projectile is launched y 0 : the initial height of the projectile d: the total horizontal distance travelled by the projectile
Example The punter on a football team tries to kick a football with an initial velocity of 25.0 m/s at an angle of 60.0º above the ground, what range (d x ) does it travel? 60 o
Example The punter on a football team tries to kick a football with an initial velocity of 25.0 m/s at an angle of 60.0º above the ground, what range (d x ) does it travel? 60 o
Example The punter on a football team tries to kick a football with an initial velocity of 25.0 m/s at an angle of 60.0º above the ground, what range (d x ) does it travel? 60 o
The punter on a football team tries to kick a football with an initial velocity of 25.0 m/s at an angle of 60.0º above the ground, what range (d x ) does it travel? 60 o
The punter on a football team tries to kick a football with an initial velocity of 25.0 m/s at an angle of 60.0º above the ground, what range (d x ) does it travel? 60 o
Another kind of problem (but you do it the same manner) The narrowest strait on earth is the Seil Sound in Scotland, which lies between the mainland and the island of Seil. The strait is only about 6.0m wide. Suppose an athlete wanting to jump over the sea leaps at an angle of 35 o with respect to the horizontal. What is the minimum initial speed that would allow the athlete to clear the gap? Neglect air resistance.
Jumping over the sea 1. Given: x = 6m θ = 35 o a y = -9.81 m/s 2 x y x = 6m y = 0 m,?? v ix = v i cos θ v iy = v i sin θ a x = 0 m/s 2 a y = -9.81 m/s 2 v θ = 35 o x = 6m
Jumping over the sea x y x y x = 6m y = 0 m,?? v ix = v i cos θ v iy = v i sin θ a x = 0 m/s 2 a y = -9.81 m/s 2 v θ = 35 o x = 6m
Jumping over the sea x y v θ = 35 o x = 6m
Jumping over the sea What was the time for the jump? Use this: What was the height of the jump? v θ = 35 o Use this x = 6m
45º will get you the greatest range Range is d x Horizontal displacement
Besides 45º, two sister angles will give you the same range 45º is would give you the greatest d x Any similar degree variation on either side of 45º would give you the same d x These would give you the same d x. 40º and 50º 30º and 60º 15º would give you the same range as what?
Classwork/Homework Practice 3F pg 109 Due Friday, 7 Oct Chapter 3 exam Monday, 10 Oct