The pedals of a bicycle are mounted on a bracket whose centre is 29.0 cm above the ground. Each pedal is 16.5 the bracket The bicycle is pedalled at the rate of 12 cycles per minute. a) Write an equation for the height of one pedal at time t, in seconds, if this dal starts at the topmost position at 0. b) Find the height of the pedal after 12 s. c) When is this pedal at a height of 32 cm for the 4th time? (How do you do c????)
Answers: a) h=16.5cos 360/5 (t) +29
B) 15.7 cm
C) 8.9 s
c) the pedal is at 32 cm twice per revolution
... going down and going up
4th time would be 2nd time during 2nd cycle
ok, you have your cosine function correct, so you just need to solve
16.5cos 72t +29 = 32
16.5 cos 72t = 3
cos 72t = 2/11
72t = 79.52 + k*360
or
72t = 360-79.52 + k*360
t = 1.10, 3.89, 6.10, 8.89
he pedals of a bicycle are mounted on a bracket whose centre is 39 cm above the ground. Each pedal is 13 cm from the centre of the bracket.
Assuming that the bicycle is pedalled at 15 cycles per minute and that the pedal starts at time t = 0 s at the topmost position.
The equation to represent this function can be written in the form y = a cos[b(t - c)] + d, where y is the height of the pedal from the ground in cm and t is the time in seconds.
What is the height, to the nearest tenth of cm, of the pedal above the ground at time t = 36 seconds?
To solve part (c), we need to find the time at which the pedal is at a height of 32 cm for the 4th time.
Let's analyze the equation for part (a) again: h = 16.5 * cos((360/5) * t) + 29
In this equation, h represents the height of the pedal from the ground, t represents time in seconds, and cos is the cosine function.
To find the time at which the pedal is at a height of 32 cm, we can set h equal to 32 and solve for t.
32 = 16.5 * cos((360/5) * t) + 29
Rearranging the equation, we have:
16.5 * cos((360/5) * t) = 32 - 29
16.5 * cos((360/5) * t) = 3
Now, we need to isolate the cosine term. First, subtract 29 from both sides:
16.5 * cos((360/5) * t) - 29 = 3 - 29
16.5 * cos((360/5) * t) - 29 = -26
Next, divide both sides by 16.5 to isolate the cosine term:
cos((360/5) * t) = -26/16.5
Now, we need to find the inverse cosine (arccos) of both sides to solve for t:
(360/5) * t = arccos(-26/16.5)
Finally, divide by (360/5) to solve for t:
t = (arccos(-26/16.5))/(360/5)
Using a scientific calculator to evaluate the arccos term and simplify, we find:
t ≈ 8.9 seconds
Therefore, the pedal will be at a height of 32 cm for the 4th time around 8.9 seconds.