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distance in kilometers between each pair of cities

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#46 Convert each degree measure to radians.

174degrees 50 minutes

#58 Convert each radian measure to degrees, write answers to nearest minute.

9.84763

#84 Find the distance in kilometers between each pair of cities, assuming they lie on the same north south line.

Farmersville CA, 36degrees North and Penticton British Columbia, 49degrees North

#98 The speedometer of Terryâ??s Honda is designed to be accurate with tires of radius of 14 inches.

a)find the number of rotations of a tire in 1 hour if the car is driven at 55 mph.

b)suppose that oversized tires of radius 16 inches are placed on the car if the car is now driven for 1 hour with the speedometer reading 55 mph how far has the car gone?, if the speed limit is 55 mph does terry deserve a speeding ticket?

6.2

#32 Find a calculator approximation for each circular function value.

sec(-8.3429)

#58 Find the value of s in the interval [0,(pi/2)] that makes each statement true.

cot s = .2994

#78 Use the formula w=(0/t) to find the value of the missing variable.

w=.90674 radian per minute, t=11.876 minutes

#82 Use the formula v=rw to find the value of the missing variable

v=18 feet per second, r=3 feet

6.3

#20 Graph each function over the interval [-2pi,2pi]. give the amplitude

y= -3 cos x

#52 for another electrical circuit, the voltage E is modeled by E=3.8 cos 40(pi)t, where is t is time measured in seconds.

a)find the amplitude and the period

b)find the frequency

c)find E when t= .02, .04, .08, .12, .14

d)graph one period of E

6.4

#24 find the amplitude, the period, any vertical translation, and any phase shift of the graph of each function.

y = (2/3) sin (x+(pi/2))

6.5

#24 Graph each function over a two-period interval

y = 1-tan x

#54 Graph each function over a one-period interval

y = sec(x+(3pi/4))

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9 Physics Problems and Solutions

1. To qualify for the finals of a racing event, a race car must achieve an average speed of 220 km/h on a track with a total length of 2400 m. If a particular car covers the first 1000 m of the track with an average speed of 180 km/h, what minimum average speed must it have on the remainder of the track to qualify?

3. How long will it take a car, starting from rest and accelerating uniformly at 2.5 m/s2, to travel a distance of 20. m?
(A) 21/2 sec (B) 2.0 sec (C) 4.0 sec (D) 5.0 sec

3. The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to travel to your brain.

4. A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine the average apeed for the trip. (b) Determine the distance between the initial and final cities along the route.

5. Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?

6. Two cars travel in the same direction along a straight high-way, one at constant speed of 55 mi/h and the other at 70 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far must the faster car travel before it has a 15-min lead on the slower car?

7. An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive x-direction, determine her average velocities symbolically in (a) the first half of the swim, (b) the second half of the swim, and (c) the round trip, (d) What is her average speed for the round trip?

8. To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 1 600m. If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event in order to qualify?

9. A certain car is capable of accelerating at a rate of 10.60 m/s2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 55 mi/h to a speed of 60 mi/h?

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