Brain Teaser Nico purchased a camera, a ruler, and an ice cream bar for $53. He paid $52 more for the camera than the ice cream bar, and the ruler cost twice as much as the ice cream bar. What did he pay for each?

Projectile Motion Ms. Bartlett November 10-11, 2015

Projectile Motion  If you observed the movement of a golf ball being hit from a tee, a frog hopping, or a free throw being shot with a basketball, you would notice that all of these objects move through the air along similar paths, as do baseballs, arrows, and bullets.  Each path is a curve that moves upward for a distance, and then, after a time, turns and moves downward for some distance.  You may be familiar with this curve, called a parabola, from math class.

Projectile Motion An object shot through the air is called a projectile.  A projectile can be a football, a bullet, or a drop of water.  You can draw a free-body diagram of a launched projectile and identify all the forces that are acting on it.

Projectile Motion  No matter what the object is, after a projectile has been given an initial thrust, if you ignore air resistance, it moves through the air at a constant velocity.  The force of gravity is what causes the object to curve downward in a parabolic flight path.  Its path through space is called its trajectory.

Trajectories Depend upon the Viewer  The path of the projectile, or its trajectory, depends upon who is viewing it.  Suppose you toss a ball up and catch it while riding in a bus. To you, the ball would seem to go straight up and straight down.  But an observer on the sidewalk would see the ball leave your hand, rise up, and return to your hand, but because the bus would be moving, your hand also would be moving. The bus, your hand, and the ball would all have the same horizontal velocity.

Projectile Motion All objects, when ignoring air resistance, fall with the same acceleration, g = 9.8 m/s 2 downward. The distance the ball falls each second increases because the ball is accelerating downward. The velocity also increases in the downward direction as the ball drops. This is shown by drawing a longer vector arrow for each time interval.

Projectile Motion Vectors can also be used to represent a ball rolling horizontally on a table at a constant velocity. Newton’s 1st Law tells us the ball will continue rolling in a straight line at constant velocity unless acted on by an outside force. Each vector arrow is drawn the same length to represent the constant velocity. The velocity would remain constant but in the real world, friction makes it slow down and eventually stop.

Projectile Motion Now, combine the motion of the ball in free fall with the motion of the ball rolling on the table at a constant velocity. This is seen when rolling the ball off of the table. The ball rolling on the table would continue forever in a straight line if gravity is ignored. The ball in free fall would continue to increase its speed if air resistance is ignored.

Projectile Motion Since the ball is moving at a constant velocity and in free fall at the same time, the horizontal and vertical vectors are added together during equal time intervals. This is done for each time interval until the ball hits the ground. The path the ball follows can be seen by connecting the resultant vectors.

Projectile Motion Look at the components of the velocity vectors. The length of the horizontal component stays the same for the whole time. The length of the vertical component increases with time.

Projectile Motion How do we combine the horizontal and vertical components to find the velocity vector? v = √ v 2 x + v 2 y

Projectile Motion Project Driving Question: To what extent can you calculate with precision the time and average horizontal and vertical velocities of a projectile launched at a waste basket 2 meters away? Note: Must do this at least 20 times for accuracy and precision.