Physics

 A projectile is any object that has been launched with no means of controlling its own flight…it is in free-fall motion while at the same time may be moving horizontally.  Everything about the projectile’s flight can be predicted from initial conditions of the launch (launch angle and speed).

 The path of a projectile is called its trajectory.  Mathematically, the shape of the trajectory is a parabola.  The projectile’s motion is a combination of horizontal and vertical motion, BUT THESE MOTIONS ARE INDEPENDENT OF EACH OTHER

 Horizontal Motion is constant (assuming no air resistance)…no horizontal acceleration!!!  At any point in a projectile’s path, horizontal velocity is the same as initial horizontal velocity

 For an object moving with constant velocity…  x = vt  x = change in position of object after time, t v = velocity of object t = elapsed time This model came from the Tumble Buggy Lab and describes exactly how a projectile moves horizontally

 Vertical motion of a projectile changes because the force of gravity acts vertically causing objects to accelerate downward at a constant rate of 10 m/s 2  On the way down, vertical speed increases 10 m/s for each second of falling.  If a projectile is on the way up, vertical speed will decrease 10 m/s for every second of “falling” until it reaches a speed of zero at the peak of its motion

 For an object that is constantly accelerating…  x = ½ at 2 + v o t v = at + v o  x = change in position after time, t a = acceleration v – velocity after time, t v o = starting velocity t = elapsed time These models came from the Ball On a Ramp lab and describe what a projectile is doing vertically

Horizontal Motion Vertical Motion Forces (present? Yes or no?) (if present, which direction?) NoYes Downward Acceleration (present? Yes or no?) (if present, which direction?) NoYes Downward Velocity (constant or changing) ConstantChanging

The velocity at any point along the trajectory is just the vector sum of the horizontal and vertical components The instantaneous direction is tangent to the path at any location

 One dimensional motion equations still apply even though projectiles move in more than one dimension.  Always keep the horizontal information separate from the vertical information in the problem.  Use your knowledge of vectors to resolve the initial velocity into its x- and y-components whenever the projectile is launched at an angle

a. Determine how much time it takes to fall. b. Determine how far from the base of the cliff it is when it hits the ground.

 Determine the initial horizontal velocity of the soccer ball.

 How tall is the building?

 How far downrange will the bullet hit the ground?

a. Find the range of the ball. b. Find the maximum height of the ball.

a. Find its “hang time” (time that the ball is in t he air). b. Find the distance the ball travels before it hits the ground. c. Find its maximum height.

 Find its position and velocity after 8.00 s.

 Find the time required to reach its maximum height.

 Find the range of the projectile.