1 . | v impact.A | > | v impact.B | 2 . | v impact.A | < | v impact.B |

1. First, review the use of the constant-acceleration kinematics equations: From a bridge high above a river, ball A is thrown straight up with initial speed |vi|. Ball B is thrown straight down with the same initial speed, |vi|. Each ball hits the water. Assuming negligible air drag, compare their impact speeds. 1. |vimpact.A|> |vimpact.B| 2. |vimpact.A|< |vimpact.B| 3. |vimpact.A|= |vimpact.B| 4. There is not enough information (“it depends”). OSU PH 211, Before Class 5

2. First, review the use of the constant-acceleration kinematics equations: From a bridge high above a river, ball A is thrown straight up with initial speed |vi|. Ball B is thrown straight down with the same initial speed, |vi|. Each ball hits the water. Assuming negligible air drag, compare their impact speeds. 1. |vimpact.A|> |vimpact.B| 2. |vimpact.A|< |vimpact.B| 3. |vimpact.A|= |vimpact.B| 4. There is not enough information (“it depends”). OSU PH 211, Before Class 5

3. The motion in each dimension acts independent of the other. OSU PH 211, Before Class 5

4. A ball is dropped from rest from the same height from which a bullet is fired horizontally over level ground. Neglecting any effects of air or topography, which would hits the ground first? • The bullet hits the ground first. • The ball hits the ground first. • They both hit at the same time. OSU PH 211, Before Class 5

5. A ball is dropped from rest from the same height from which a bullet is fired horizontally over level ground. Neglecting any effects of air or topography, which bullet hits the ground first? • The bullet hits the ground first. • The ball hits the ground first. • They both hit at the same time. OSU PH 211, Before Class 5

6. 2-Dimensional Motion (with Constant Acceleration) The four equations of kinematics help us describe and calculate the motion of any object undergoing constant acceleration (including zero acceleration) with respect to any single axis. But what if that object is moving relative to two axes at once? The vector nature of displacement, velocity and acceleration let us calculate the x- and y- motions separately. For the motion along each axis, we use the respective vector components (x, vx.i, vx.f, and axory, vy.i, vy.f, and ay). The one consistent connection between the two parts of the motion is time: We’re talking about one object, so the same time interval, t, applies to both x- and y- motions. OSU PH 211, Before Class 5

7. x-motiony-motion vx.f = vx.i+ax(t) vy.f = vy.i+ay(t) x = (1/2)(vx.i+vx.f)t y = (1/2)(vy.i+vy.f)t x = vx.i(t)+(1/2)ax(t)2y = vy.i(t)+(1/2)ay(t)2 vx.f2 = vx.i2+2ax(x)vy.f2 = vy.i2+2ay(y) (t is common to both motions.) ax is constantay is constant OSU PH 211, Before Class 5

8. Could you now use the kinematics equations of constant acceleration (twice—once for each axial direction) to answer questions such as these? A baseball player friend of yours wants to determine how fast she can throw a baseball. You have her stand on a flat roof and throw the ball horizontally. The ball is released 4m above the ground and it lands 25 meters away. How fast did she throw the ball? How fast did it hit the ground? See if you can describe your solutions here (in words). Be sure to explain how you know they are correct. OSU PH 211, Before Class 5