SOLUTION: The equation h(t)=40sin(5π/4 t- π/2)+55
describes the height, H in cm, that the centre of a yo-yo is above the ground, during standard motion, as a time in seconds.
Use
Algebra.Com
Question 725616: The equation h(t)=40sin(5π/4 t- π/2)+55
describes the height, H in cm, that the centre of a yo-yo is above the ground, during standard motion, as a time in seconds.
Use the equation to determine the:
(i) length of the string.
(ii) smallest distance between the yo-yo and the ground
(iii) the time taken to complete one swing
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(i) The length of the string would be the distance between the highest point (the hand) and the lowest point. The distance between the maximum and the minimum of a sin graph is twice the amplitude. The 40 in the equation is the amplitude so the length of the string is 80 cm.
(ii) The minimum value for a sin function (with a positive coefficient like 40) will occur when sin has its minimum value. The minimum value of a sin is -1. Replacing the sin with -1 we can find the minimum height:
40(-1) + 55 = 15 cm
(iii) The time it takes to for one complete swing/cycle is the period of the function. In a sin equation like this one, the period is related to the coefficient of x (called "B") by the equation:
B = 2pi/period
The "B" in our equation is so:
/period
Now we can solve for the period. Multiplying both sides by the period:
(period)*
Dividing both sides by :
period =
which simplifies to:
period = 8/5
So it takes 8/5 (or 1.6) seconds for one complete cycle.
RELATED QUESTIONS
The equation ( ) 40sin 5 55
4 2
h t = ⎛⎜ π t −π... (answered by Alan3354)
The equation h(t)=40sin(5π/4 t - π/2)+55 describes the height, H in cm, that... (answered by Alan3354)
Using equation : h(t)=40sin(5π/4 t - π/2)+55
Describe the transformation(s) (answered by Alan3354)
The equation h(t) = 40 sin(5pi/4 t - pi/2) + 55
I have worked out the length of string (answered by lynnlo)
A ball is thrown upward with an initial velocity of 64 ft/sec from a height of 960 ft.... (answered by ankor@dixie-net.com)
The height of an object is given by the equation: h = 20-4 cos2πt, where h is height (answered by Alan3354)
As a bird flies upward, it drops a berry at a height of 600 feet above the ground. The... (answered by nerdybill)
Lydia holds the end of a yo-yo string 0.9 metres from the ground and swings the yo-yo in... (answered by ikleyn)
The equation that describes the path of a rocket after it is shot in the air is... (answered by Earlsdon)