Problem 67
New York City is roughly \(4800 \mathrm{~km}\) from Seattle. When it is 10:00 A.M. in Seattle, it is 1:00 P.M. in New York. Using this information, estimate (a) the rotational speed of the surface of Earth, (b) the circumference of Earth, and (c) the radius of Earth.
Problem 70
The light that plants absorb to perform photosynthesis has a wavelength that peaks near \(675 \mathrm{~nm}\). Express this distance in (a) millimeters and (b) meters.
Problem 71
On June 9, 1983, the lower part of the Variegated Glacier in Alaska (Figure 1.16) was observed to be moving at a rate of \(64 \mathrm{~m}\) per day. What is this speed in kilometers per hour?
Problem 73
When Coast Guard pararescue jumpers leap from a helicopter to save a person in the water, they like to jump when the helicopter is flying "ten and ten," which means it is 10 feet above the water and moving forward with a speed of 10 knots. What is "ten and ten" in SI units? (A knot is 1 nautical mile per hour, and a nautical mile is \(1.852 \mathrm{~km}\).)
Problem 74
Type A nerve fibers in humans can conduct nerve impulses at speeds up to \(140 \mathrm{~m} / \mathrm{s}\) (see Figure 1.17). (a) How fast are the nerve impulses moving in kilometers per hour? (b) How far (in meters) can the impulses travel in \(5.0 \mathrm{~ms}\) ?
Problem 75
The mass of a newborn baby's brain has been found to increase by about \(1.6 \mathrm{mg}\) per minute. (a) How much does the brain's mass increase in 1 day? (b) How long does it take for the brain's mass to increase by \(0.0075 \mathrm{~kg}\) ?
Problem 76
On December 25,2004 , during a NASA mission to Saturn, the spacecraft Cassini released a probe named Huygens, which landed on the Saturnian moon Titan on January 14,2005 . Huygens was released from the main spacecraft at a gentle relative speed of \(31 \mathrm{~cm} / \mathrm{s}\). As Huygens moved away, it rotated at a rate of seven revolutions per minute. (a) How many revolutions had Huygens completed when it was \(150 \mathrm{~m}\) from Cassini? (b) How far did Huygens move away from Cassini during each revolution? Give your answer in meters.
Problem 76
On December 25, 2004, during a NASA mission to Saturn, the spacecraft Cassini released a probe named Huygens, which landed on the Saturnian moon Titan on January 14,2005 . Huygens was released from the main spacecraft at a gentle relative speed of \(31 \mathrm{~cm} / \mathrm{s}\). As Huygens moved away, it rotated at a rate of seven revolutions per minute. (a) How many revolutions had Huygens completed when it was \(150 \mathrm{~m}\) from Cassini? (b) How far did Huygens move away from Cassini during each revolution? Give your answer in meters.
Problem 77
Acceleration is related to velocity and time by the following expression: \(a=v t^{p}\). Find the power \(p\) that makes this equation dimensionally consistent.
Problem 78
The period \(T\) of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is \(L\) and the acceleration due to gravity is \(g\), then the period is given by $$ T=2 \pi L^{p} g^{q} $$ Find the powers \(p\) and \(q\) required for dimensional consistency.
