Question

1.A child is on a swing. At its highest point, the swing is 5 feet above the ground. At its lowest point, the swing is 2 feet above the ground. At its midpoint, the swing is 3.5 feet above the ground. The height of the swing above the ground is represented ℎ(?) + 3.5. The swing starts at its lowest point and it takes 2? seconds for the swing to go from the lowest point, to the highest point, and back again. What is the height of the swing when ? = ?/2

2. A child is on a swing. At its highest point, the swing is 5 feet above the ground. At its lowest point, the swing is 2 feet above the ground. At its midpoint, the swing is 3.5 feet above the ground. The height of the swing above the ground is represented by ℎ(?) + 3.5. The swing starts at its lowest point and it takes 2? seconds for the swing to go from the lowest point, to the highest point, and back again. Which of the following values of ? correspond to the highest point on the swing?

a) 0

b) ? 2

c) ?

d) 3? 2

3. A child is on a swing. At its highest point, the swing is 5 feet above the ground. At its lowest point, the swing is 2 feet above the ground. At its midpoint, the swing is 3.5 feet above the ground. The height of the swing above the ground is represented by ℎ(?) + 3.5. The swing starts at its lowest point and it takes 2? seconds for the swing to go from the lowest point, to the highest point, and back again. What is the amplitude of ℎ(?)?

4. A child is on a swing. At its highest point, the swing is 5 feet above the ground. At its lowest point, the swing is 2 feet above the ground. At its midpoint, the swing is 3.5 feet above the ground. The height of the swing above the ground is represented by ℎ(?) + 3.5. The swing starts at its lowest point and it takes 2? seconds for the swing to go from the lowest point, to the highest point, and back to the lowest point. Which of the following functions could be ℎ(?)?

a) 1.5 sin ?

b) −1.5 sin ?

c) 1.5 cos ?

d) −1.5 cos t

Answer 1

4)The height of the swing above the ground is represented as   where since satisfies all the given conditions.

Answer is (d).

Thus, .

1)The height of the swing when is

2) The function is maximum at .

Thus,   correspond to the highest point on the swing.

Answer is (c).

3) Since , the amplitude of is .