Lab 05 – Freefall Paths Purpose Students will observe and analyze the parabolic paths of freefall. Theory Freefall occurs any time an object is entirely unsupported in a gravitational field. (Planes are supported by forces from the wind, of course.) Even if the unsupported object is going upwards, gravity is hammering down the whole time, slowing it until it begins to fall, then speeding it toward the ground. If its downward speed grows linearly, its vertical descent is proportional to t². Gravity doesn’t act horizontally, so any lateral speed will be constant. This means every freefall path is parabolic or part of a parabolic arc. For an object thrown straight up, the parabola is too skinny to recognize, but it is still there. Rounding gravity’s acceleration to a friendly 10 m/s², there are really just two key equations for freefall: v = 10t and y = 5t² (truly 9.8t and 4.9t²). Both measure relative to the highest point in the parabolic arc—its apex. So v is the vertical speed only, y gives the descent distance (down is positive) and t is the time before or after reaching the apex. Suppose, for example, a cannon is fired diagonally upward from the edge of a cliff 35 m high and lands below. If it’s given that the initial upwards speed was 30 m/s, a parabola can be drawn as shown, and t₁ is 30/10 = 3 s, and so y₁ = 5(3)² = 45 m. These are the time and distance to the apex, marked as a red bullseye. On the other side, then, y₂ is 45 35 = 80 m, so t₂ = √(80/5) = 4 s, and v₂ = 10·4 = 40 m/s. Everything is now known about this parabola! Figure 05: The parabola described. Procedure 1. Wad up a piece of paper and toss it at various angles up and down trying to get it to follow any freefall path other than that of a parabola or part of one. Analysis Please answer all of the following in Canvas with complete sentences. Yes, these simple questions really do need complete sentences as answers. 1. What is the vertical component of the speed at the apex of any parabola? 2. If the acceleration at that apex were equal to zero, it would mean the speed never changed up there. Based on that fact, use the answer from question 1 to describe what objects thrown upward would do after reaching their highest point if the speed never changed again. That is, how would they behave? 3. At what point in the entire freefall parabola is the acceleration NOT equal 9.8 m/s² downwards? Think carefully before answering this one! 4. If the speed of an object going along a freefall parabola at a given height is 10 m/s going up, what will its speed be at the same height on the way down?