2 Freely Falling Objects An object is in free fall when it accelerates downward only under the influence of gravityAir resistance must be removedThis is an idealization, not applicable to real-world situationsThe object is in free fall as soon as it is released, whether it is dropped, thrown downward, or thrown upwardALL OBJECTS UNDERGOING FREE FALL HAVE THE SAME ACCELERATION, RAGARDLESS OF SHAPE OR MASS!!!!!!!
3 Free Fall Acceleration Acceleration due to gravity is denoted by the letter gThe value of g varies by location, see table belowWe will use the valueg = 9.81 m/s2
4 Free Fall Acceleration The acceleration that all objects experience is a result of the force of gravityAcceleration due to gravity, g, near the surface of the earth is 9.8 m/s2
5 Free Fall Kinetematic Equations Because a = -g for free fall and we use y instead of x, we have the following
6 Position EquationThe equation that describes an object’s vertical position as a function of timeis a quadratic equationThe constants are: A = -½g, B = vi, C = yiThe P vs T graph should always be a downward-opening parabola
7 Velocity EquationThe equation for an object’s velocity as a function of time is linearThe slope of the line will be m = -gThe y-intercept will be b = viThe graph will always be a downward-sloping line
8 Example 1 A ball is thrown upward with a velocity of 40 m/s. Find its velocity after 2 s.Find its height after 2 s.
9 Example 1 A ball is thrown upward with a velocity of 40 m/s. Find its velocity after 7 s.Find its height after 7 s.
10 At max heightAt an object’s maximum height, its velocity will change from positive to negative and therefore be zero (vf = 0)Use this fact to calculate the time at max height using the equationOr use this fact to calculate the max height using the equation
11 Example 1 A ball is thrown upward with a velocity of 40 m/s. What is the ball’s maximum height?How long does it take the ball to reach maximum height?
12 Example 1 A ball is thrown upward with a velocity of 40 m/s. How long is the ball in the air?How fast is the ball going just before it hits the ground?
13 Example 2A volleyball player hits a volleyball so that it moves upward with a velocity of 6 m/s straight upward. The volleyball starts 2 m above the floor. -How long will it be in the air before it hits the ground? -Find the ball’s maximum height above the floor.
14 Example 3A baseball player hits a popup straight up and it remains in the air for 6 seconds before it is caught by the catcher. The bat made contact with it at 1.5 m above the ground and the catcher caught it only 0.25 m above the ground. -Find the ball’s initial velocity. -Find the ball’s maximum height
15 Example 4A ball is dropped from a tower 70 m high. -Find the ball’s velocity after 1 s, 2 s, and 3 s of freefall. -Find the ball’s height after 1 s, 2 s, and 3 s of freefall.
16 Example 5A ball is thrown downward with a speed of 25 from a tower 70 m high. -Find the ball’s velocity after 1 s, 2 s, and 3 s of freefall. -Find the ball’s height after 1 s, 2 s, and 3 s of freefall.
17 Example 6A person steps off the end of a 3.00-m-high diving board and drops to the water below. (a) How long does it take of the person to reach the water? (b) What is the person’s speed on entering the water?
18 Example 7A volcano shoots out blobs of molten lava called lava bombs, from its summit. A geologist observing the eruption uses a stopwatch to time the flight of a particular lava bomb that is projected straight upward. If the time for it to rise and fall back to the ground is 5.25 s, what is it’s initial speed?
19 Free Fall GraphingShow the region on the above graph where the object is moving upwardShow the region on the above graph when the object is moving downwardShow the point on the graph where the object has reached its maximum heightWhat is the object’s initial velocity?
20 Free Fall GraphingShow the region on the above graph where the object is moving upwardShow the region on the above graph when the object is moving downwardShow the point on the graph where the object has reached its maximum height
21 Analyzing the Motion of an Object in Free Fall Notice:The motion is symmetrical about the object’s maximum heightThe slope is zero at the object’s maximum heightTherefore, the object’s velocity is zero at max heightThe slope is equal (but opposite) at the same heightTherefore, objects have the equal speed at the equal heights