The ladder problem investigated in Lesson 16.1 is modified in this lesson to take into account the force of gravity on the ladder.
Suppose the fifteen-foot ladder from Lesson 16.1 is held against a wall and the top of the ladder is being pulled downward by the force of gravity. The equation below models the position of the top of the ladder where the term -16t2 represents the motion of the top of the ladder due to gravity and 15 represents the position of the top at time t = 0 seconds.
The equation for the position of the bottom of the ladder can be found using the Pythagorean theorem.
16.2.1 Write the parametric equations that model the position of the top and bottom of the ladder at time t. Click here for the answer.
Displaying the Model
- Enter the parametric equations found in Question 16.2.1 in the Y= Editor.
- Choose Animate for the Graph style for both pairs of equations.
- Make sure "Simultaneous" is still the Graph Order on the MODE screen.
- Graph the equations in a [0, 1, 0.05] x [-1, 16, 1] x [-1, 16, 1] window.
16.2.2 Describe the apparent motion of the top and bottom of the ladder. Click here for the answer.
16.2.3 How fast is the bottom of the ladder moving at t = 0.2, t = 0.5 and t = 0.8 seconds? Click here for the answer.