NEED HELP WITH QUESTION 6 6 Write an equation for the height

NEED HELP WITH QUESTION 6.

6) Write an equation for the height of the point P above the ground as a function of t, time in seconds. ______________?????

A wheel with radius 2 cm is being pushed up a ramp at a rate of 7 cm per second. The ramp is 700 cm long, and 100 cm tall at the end. A point P is marked on the circle as shown (picture is not to scale).

700 cm

100 cm

1) How far does the wheel travel in one rotation? 4 pi

2) Traveling at 7 cm/sec, how long does it take the wheel to complete one rotation. 4pi/7

3) What is the initial height of the center of wheel? 2

4) Traveling at 7 cm/sec, in one second, how much does the height of the center of wheel increase? 1

5)   Write an equation for the height of the center of the wheel as a function of t, time in seconds. 1(t) +2

Solution

1) radius of the wheel is 2

in one rotation distance travelled 2pi*r

= 2*pi*2

= 4pi

2) speed = 7cm / sec

time to complete one rotation is

time = distance / speed

time = 4pi / 7 seconds

3) initial height of the center of the wheel is the distance from cehter to one end

which is the radius = 2

4) height increases by 100/ 700 * 7

= 1 cm

5) equation = 7* ( 100 / 700 ) t + 2

equation 1t + 2