Question

A child wanders slowly down a circular staircase from the top of a tower. With in feet and the origin at the base of the tower, her position minutes from the start is given by?

Answer 1

The position of the child can be determined using the equation x = h - vt, where h is the height of the tower, and t is the time elapsed since the start.

Step-by-step explanation:

The position of the child minutes from the start can be determined using the equation:

x = x0 + vt

Where:

• x is the position of the child from the base of the tower
• x0 is the initial position of the child, which is the height of the tower
• v is the velocity of the child, which is the rate at which the child is descending
• t is the time elapsed from the start

Since the child is wandering slowly down the staircase, we can assume a constant velocity. Let's say the velocity is -v (negative because it is downward).

Therefore, the equation becomes:

x = h - vt

Where h is the height of the tower, and t is the time elapsed since the start.

Answer 2

The child's position on the circular staircase is determined by the angle of rotation and the radius of the staircase. The position can be calculated using the formula for angular displacement.

Step-by-step explanation:

The child's position on the circular staircase can be determined by the angle of rotation and the radius of the staircase. Let's assume that the child takes t minutes to reach a certain position on the staircase. In t minutes, the child would have traveled t/60 of a full revolution around the circular staircase. Since there is a direct relationship between the angle of rotation and the position of an object on a circular path, we can use the formula for angular displacement to find the child's position.

Angular Displacement = Angle of Rotation x Radius of Staircase

Position = (t/60) x 2πr

So, the position of the child in feet from the base of the tower after t minutes is (t/60) x 2πr feet.