A wheel with radius 4 cm is being pushed up a ramp at a rate of 8 cm per second. The ramp is 760 cm long, and 250 cm tall at the end. How far does thw wheel Traveling at 8 cm/sec.How long does it take the wheel to complete one rotation. What is the initial height of the center of wheel.Traveling at 8 cm/sec, in one second, how much does the height of the center of wheel increase.Write an equation for the height of the center of the wheel as a function of t, time in seconds.Write an equation for the height of the point P above the ground as a function of t, time in seconds
To answer these questions, we need to break down the problem and use some basic formulas.
1. How far does the wheel travel when traveling at 8 cm/sec?
The distance traveled can be calculated using the formula: distance = rate × time. So, if the wheel is traveling at 8 cm/sec for a certain amount of time, let's say t seconds, then the distance traveled will be 8 cm/sec × t sec = 8t cm.
2. How long does it take the wheel to complete one rotation?
To find the time it takes for one rotation, we need to use the formula: circumference = 2πr, where r is the radius of the wheel. In this case, the radius is given as 4 cm. So, the circumference would be 2π × 4 cm = 8π cm. Since the wheel is traveling at a rate of 8 cm/sec, the time it takes for one rotation would be (8π cm) / (8 cm/sec) = π seconds.
3. What is the initial height of the center of the wheel?
The initial height of the center of the wheel is given as 250 cm.
4. Traveling at 8 cm/sec, in one second, how much does the height of the center of the wheel increase?
Since the wheel is going up a ramp, the height of the center of the wheel will increase as it moves along the ramp. For every 1 cm it travels horizontally, it will also increase vertically. So, the increase in height when traveling at 8 cm/sec for one second would be 8 cm.
5. Writing an equation for the height of the center of the wheel as a function of t, time in seconds.
The height of the center of the wheel can be represented as h(t) = 250 + 8t, where h(t) is the height at time t.
6. Writing an equation for the height of the point P above the ground as a function of t, time in seconds.
The height of the point P above the ground will depend on both the initial height of the center of the wheel and the height it gains along the ramp. So, the equation for the height of point P can be represented as P(t) = 250 + 8t.