Sketch what you see—for each of these observations:

1. Sketch what you see—for each of these observations: • The motion of the cart with respect to the table • The motion of the ball with respect to the cart • The motion of the ball with respect to the table Oregon State University PH 211, Lecture #7

2. A ball is dropped from rest from the same height from which a bullet is fired horizontally. Neglecting any effects of air or topography, which hits the ground first? • The bullet hits the ground first. • The ball hits the ground first. • They both hit at the same time. Oregon State University PH 211, Lecture #7

3. The motion in each dimension acts independent of the other. Oregon State University PH 211, Lecture #7

4. A car passes by you at a constant velocity of 20 m/s (over level ground), just as you fire a pellet from a gun. The pellet leaves the gun at an initial speed of 40 m/s. At what initial angle (above the horizontal) would the gun need to be aimed in order for the pellet to hit the car? 1. 30° 2. 60 ° 3. 15 ° 4. 45 ° 5. None of the above. Oregon State University PH 211, Lecture #7

5. 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. Oregon State University PH 211, Lecture #7

6. 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 Oregon State University PH 211, Lecture #7

7. In all cases, the actual motion of the object is the vector sum of the component motions. For example, starting with ti = 0, xi = 0 and yi = 0, notice how completely you can describe the motion: The object’s actual position at any time, t, is a vector sum: x + y (Examples: What is the pellet’s position at t = 0 s? 3 s? 4s? 8s?) The object’s actual velocity at time t is a vector sum: vx + vy (Examples: What is the pellet’s velocity at t = 0 s? 3 s? 4s? 8s?) The object’s actual acceleration at time t is a vector sum: ax + ay (Examples: What is the pellet’s acceleration at t = 0 s? 3 s? 4s? 8s?) Oregon State University PH 211, Lecture #7

8. You kick a soccer ball at a 45° angle.It goes up and down and hits the ground. What can you say about its speed at thetop of its arc? • It is 9.8 m/s2 • It is 0 m/s • It is 9.8 m/s • It is faster than immediately after the kick. • It is slower than immediately after the kick. Oregon State University PH 211, Lecture #7

9. A battleship simultaneously fires two shells at enemy ships. Assuming negligible air drag, which ship gets hit first? Oregon State University PH 211, Lecture #7

10. Which of the following variables BY ITSELF determines which ship gets hit first? • The horizontal distance the shell moves • The maximum height each shell reaches • The angle at which the shell is launched • None of the above Oregon State University PH 211, Lecture #7

11. 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? Oregon State University PH 211, Lecture #7