Algebra 2 Unit 3 Topic 1_SLT 1 Circular Motion Model

Front

What is the formula for the height of a rider on a Ferris wheel at any angle θ?

Back

h(θ) = r * sin(θ) + h0, where r is the radius and h0 is the height of the center above the ground.

Front

Define circular motion in the context of a Ferris wheel.

Back

Circular motion refers to the movement of an object along the circumference of a circle or rotation along a circular path.

Front

What is the significance of the angle in circular motion?

Back

The angle determines the position of the rider on the Ferris wheel and affects the height above the ground.

Front

How do you calculate the height of a rider at 65 degrees on a Ferris wheel with a radius of 40 m and center height of 30 m?

Back

h(65) = 40 * sin(65) + 30 ≈ 67.19 m.

Front

What is the relationship between rotational speed and the sine function in the context of Ferris wheel motion?

Back

Increasing the rotational speed multiplies the angle in the sine function, affecting the height and position of the rider.

Front

What is the height of a rider at 0 degrees on a Ferris wheel with a radius of 40 m and center height of 30 m?

Back

h(0) = 40 * sin(0) + 30 = 30 m.

Front

If a Ferris wheel rotates at 36t instead of 4t, what does this indicate about its speed?

Back

It indicates that the Ferris wheel is rotating 9 times faster than the original speed.

Front

What is the shortest distance from the start to the ground on a Ferris wheel with a center height of 30 m and radius of 40 m?

Back

The shortest distance is the height of the center minus the radius: 30 m - 40 m = -10 m (not possible, so the minimum height is 0 m).

Front

How can you find another angle that gives the same height as 65 degrees?

Back

Use the property of sine: sin(θ) = sin(180° - θ). For 65°, the other angle is 115°.

Front

What is the height of a rider after 10 seconds if the Ferris wheel completes one rotation every 20 seconds?

Back

Calculate the angle after 10 seconds: θ = (10/20) * 360° = 180°. Then, h(180) = 40 * sin(180) + 30 = 30 m.