Preview Section 1 Displacement and Velocity Section 2 Acceleration Section 3 Falling Objects

Free Fall Assumes no air resistance Acceleration is constant for the entire fall Acceleration due to gravity (ag or g ) Has a value of -9.81 m/s2 Negative for downward Roughly equivalent to -22 (mi/h)/s When presenting this slide, you may wish to refer students to Figure 14 in their textbook. You could also begin this slide with a video clip of the “feather and hammer” experiment on the moon. It is available on NASA and other web sites. Perform an internet search with the terms “feather and hammer on moon” to find a link. Discuss the effects of air resistance with students. With air resistance, an object will continue to accelerate at a smaller rate until the acceleration is zero. At that point the object has reached “terminal velocity.”

Free Fall For a ball tossed upward, make predictions for the sign of the velocity and acceleration to complete the chart. Velocity (+, -, or zero) Acceleration When halfway up When at the peak When halfway down + - zero When presenting this slide, you may wish to refer students to Figure 15 in their textbook. You can also demonstrate the motion for students. Toss a ball up and catch it. Ask students to focus on the spot half-way up and observe the motion at that time. They can then predict the sign for the velocity and acceleration at that point. Then ask students to focus on the peak and, finally, on a point half-way down. Often students believe the acceleration at the top is zero because the velocity is zero. Point out to them that acceleration is not velocity, but changing velocity. At the top, the velocity is changing from + to -. Ask students to explain each combination above. For example, a positive velocity (moving upward) and a negative acceleration (downward) would cause the velocity to decrease.

Free Fall Click below to watch the Visual Concept. Visual Concept

Graphing Free Fall Based on your present understanding of free fall, sketch a velocity-time graph for a ball that is tossed upward (assuming no air resistance). Is it a straight line? If so, what is the slope? Compare your predictions to the graph to the right. Now students are asked to graph the motion they just observed. This graph should match the answers to the chart on the last slide. Remind them that they are graphing velocity, but acceleration is the slope of the velocity-time graph. Student graphs may have a different initial velocity and a different x-intercept (the time at which the velocity reaches zero), but their graphs should have the same shape and slope as the one given on the slide. Point out that the velocity is zero at the peak (t = 1.1 s for this graph) while the acceleration is never zero because the slope is always negative. Help them get an approximate slope for the graph shown on the slide. It should be close to -9.81 (m/s)/s.

Velocity and Acceleration of an Object at its High Point Click below to watch the Visual Concept. Visual Concept

Classroom Practice Problem A ball is thrown straight up into the air at an initial velocity of 25.0 m/s upward. Create a table showing the ball’s position, velocity and acceleration each second for the first 5 s. t (s) y (m) v (m/s) a (m/s2) 1.00 2.00 3.00 4.00 5.00 20.1 +15.2 -9.81 30.4 +5.4 -9.81 30.9 -4.4 21.6 -14.2 2.50 -24.0 The equations from Section 2 apply because this is uniform acceleration. Simply use “y” instead of “x,” and the acceleration is -9.81 m/s2. Allow students some time to get the answers for t = 1.00 s, and then show them the calculations. Then have them continue with the following rows of the table. Students can use equation (4) from the previous lecture to get y, and the second version of equation (2) to get v. Or, they could get y by using equation (1) after getting the velocity, but they must get the average before using equation (1). Point out to students that the ball turns around between the 2.00 and 3.00 second mark. This makes sense, since it starts with a velocity of 15.2 m/s and loses 9.81 m/s of it’s velocity each second (in other words, the velocity decreases by 9.8 m/s in each step).

Practice Problems Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0m above the floor, how long will it be in the air before it strikes the floor? t= 2.55s

Practice Problems Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball stats from 2.0m above the floor, how long will it be in the air before it strikes the floor? What is the displacement and velocity of the ball after 0.50s after Jason hits it? X=1.8 m and +1.1 ms

Practice Problems Stephanie serves the volleyball from a height of 0.80m and gives it an initial velocity of +7.6 m/s straight up? How high will it go? X=3.7 m

Practice Problems Stephanie serves the volleyball from a height of 0.80m and gives it an initial velocity of +7.6 m/s straight up? How long will it take the ball to reach its maximum height? t= 0.77 s

Practice Problems A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s? What will its speed be when it returns to it’s starting position? V= 8.0 m/s

Practice Problems A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s? How long will it take for it to reach its starting position? t= 1.63 s

Practice Problems A flowerpot falls from a windowsill 25.0 m above the sidewalk? How fast is the flowerpot moving when it strikes the ground? V= 22.1 m/s

Practice Problems A flowerpot falls from a windowsill 25.0 m above the sidewalk? How much time does the passerby on the sidewalk have to move out of the way before the flowerpot hits the ground? t= 2.25 s

Practice Problems A robot probe drops a camera off the rim of a 24 km deep crater on Mars, where the free fall acceleration is -3.7 m/s2. Find the time it takes for the camera to reach the crater floor and the velocity with which it hits? t= 110 s and -420 m/s

Practice Problems Maria throws an apple vertically upward from a height of 1.3 m with an initial velocity of +2.4 m/s. Will the apple reach Maria’s friend in a tree house 5.3 m above the ground? No

Practice Problems Maria throws an apple vertically upward from a height of 1.3 m with an initial velocity of +2.4 m/s. If the apple is not caught, how long will the apple be in the air before it hits the ground? 0.82 s