PHYS 2101 Chapter : Written HW 1 Solutions
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You should treat the car as a point particle, ignoring its height, length, and width. You are driving at a constant speed (cid:1)(cid:2) on a straight highway that passes under an overpass. Express your answer in terms of (cid:6), (cid:7), and any. First, you must define your choice of coordinate axes. Let the positive (cid:8)-axis point in the direction that the car is initially travelling, and let the positive (cid:9)-axis point vertically upward. Now, if the balloon hits the car, then the car must undergo the displacement (cid:10)(cid:8)(cid:4)(cid:11)(cid:6) in the same time that it takes the balloon to undergo the displacement (cid:10)(cid:9)(cid:4)(cid:12)(cid:7). Then we solve the following two displacement equations simultaneously: (cid:10)(cid:9)(cid:14)(cid:15)(cid:15)(cid:15)(cid:15)(cid:15)(cid:12)(cid:7)(cid:4)(cid:12)(cid:16)(cid:17)(cid:18)(cid:3)(cid:13)(cid:19) relevant constants. Simplify your answer as much as possible. (cid:10)(cid:8)(cid:14)(cid:15)(cid:15)(cid:15)(cid:15)(cid:15)(cid:15)(cid:6)(cid:4)(cid:1)(cid:2)(cid:3)(cid:13) From the vertical displacement equation, we find that. Ignoring the unphysical negative solution, we substitute (cid:3)(cid:13) into the rearranged (cid:10)(cid:8) expression ((cid:1)(cid:2)(cid:4)(cid:6)(cid:24)(cid:3)(cid:13)) to find (cid:3)(cid:13)(cid:19)(cid:15)(cid:4)(cid:17)(cid:7)(cid:18) (cid:15)(cid:15)(cid:15)(cid:15)(cid:15)(cid:15)(cid:20)(cid:15)(cid:15)(cid:15)(cid:15)(cid:15)(cid:3)(cid:13)(cid:15)(cid:4)(cid:21)(cid:22)(cid:17)(cid:7)(cid:18)(cid:15)(cid:15)(cid:23) (cid:1)(cid:2)(cid:4) (cid:6) (cid:25)(cid:17)(cid:7)(cid:24)(cid:18)(cid:4)(cid:6)(cid:26)(cid:18)(cid:17)(cid:7)(cid:15)(cid:15)(cid:23)
