my exam is tomorrow, please help me out with this review question!!!
The diameter of a car's tire is 50cm. While the car is being driven, the tire picks up a nail.
a) Model the height of the nail above the ground in terms of the distance the car has travelled since the tire picked up the nail.
b) How high above the ground will the nail be after the car has travelled 0.5km?
c) The nail reaches a height of 10 cm above the ground for the 6th time. How far has the car travelled?
d) what assumption must you make concerning the driver's habits for the dunction to give an accurate height?
SHOW UR WORK PLEASE :(:(: :( :(
2007-07-22 15:25:21 · 1 answers · asked by mystery_girl07 2 in Science & Mathematics ➔ Mathematics
From the diameter, you get an amplitude of 25 and a vertical translation of 25, so thus far h = 25(sin or cos)(bx) + 25. Since at x = 0, h = 0, (nail at lowest point), we need cos, which we figure from peak to peak. So h = -25cos(bx) + 25. One turn of the tire, and one cycle of the nail up and down, moves the car 50π cm, so that's the wavelength, or period. x's coefficient is 2π/p, so we get 2π/50π = 1/25 (cute!). that makes h = -25 cos (t/25) + 25.
when x = 0.5 km = 500 m = 50,000 cm, h = -25 cos(50,000/25) + 25 = 27.76 cm
10 = -25cos(x/25) + 25
-15 = -25cos(x/25)
0.6 = cos(x/25)
±0.9273 + kπ = x/25
±23.182 + 25kπ = x
so the nail is at a height of 10 cm 23.18 cm after the start of each cycle and 23.18 cm before the end of each cycle. so it will be there the 6th time 23.18 cm before the end of the 3rd cycle, so 3(50π) - 23.18 = 448.06 cm.
steady speed and direction. sudden changes of speed will compress the tire.
2007-07-22 15:52:15 · answer #1 · answered by Philo 7 · 0⤊ 0⤋