Chapter 3: Q.11CQ (page 121)
Explain why a vector cannot have a component greater than its own magnitude.
The vector cannot have a component greater than its own magnitude, because the sine and cosine components are always either less than or equal to one.
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Question: Find the components of \({v_{tot}}\) along the \(x\)- and \(y\)-axes in Figure 3.55.
Figure: The two velocities \({{\rm{v}}_{\rm{A}}}\) and \({{\rm{v}}_{\rm{B}}}\) add to give a total \({{\rm{v}}_{{\rm{tot}}}}\).
Gun sights are adjusted to aim high to compensate for the effect of
gravity, effectively making the gun accurate only for a specific range.
(a) If a gun is sighted to hit targets that are at the same height as the gun andm away, how low will the bullet hit if aimed directly at a target m away? The muzzle velocity of the bullet ism/s.
(b) Discuss qualitatively how a larger muzzle velocity would affect this problem and what would be the effect of air resistance.
An athlete crosses a -m-wide river by swimming perpendicular to the water current at a speed of m/s relative to the water. He reaches the opposite side at a distance m downstream from his starting point. How fast is the water in the river flowing with respect to the ground? What is the speed of the swimmer with respect to a friend at rest on the ground?
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.)
(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.
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