Chapter 3: Q.10CQ (page 119)
Give an example of a nonzero vector that has a component of zero.
If a vector is acting along a particular axis, either x or y axis, then the component of the vector other than its direction will be zero.
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(a) Use the distance and velocity data to find the rate of expansion as a function of distance.
(b) If you extrapolate back in time, how long ago would all of the galaxies have been at approximately the same position? The two parts of this problem give you some idea of how the Hubble constant for universal expansion and the time back to the Big Bang are determined, respectively.
Two campers in a national park hike from their cabin to the same spot on a lake, each taking a different path, as illustrated below. The total distance traveled along Path 1 is 7.5km, and that along Path 2 is 8.2km. What is the final displacement of each camper?
Prove that the trajectory of a projectile is parabolic, having the form . To obtain this expression, solve the equation for and substitute it into the expression for (These equations describe the xand y positions of a projectile that starts at the origin.) You should obtain an equation of the form where a and bare constants.
In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: north of west; then south of east; then south of west; then straight east; then east of north; then south of west; and finally north of east. What is his final position relative to the island?
In the standing broad jump, one squats and then pushes off with the legs to see how far one can jump. Suppose the extension of the legs from the crouch position ism and the acceleration achieved from this position istimes the acceleration due to gravity, g. How far can they jump? State your assumptions. (Increased range can be achieved by swinging the arms in the direction of the jump.)
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