Dropdown Tower
Author: Andreas Bauer

Play animation

Time [s]

Height [m]

Difference [m]

Give hint how to calculate the average speed

Show solutions

Give hint on how to see where the gondola reaches maximum speed

The average speed is calculated by dividing the distance by the 
time:
$v_avg = \frac{\mbox{Height at beginning}  - \mbox{Height at end}}{\mbox{time needed for the path}}$

You can see that the gondola is accelerating from

        1. the slope of the graph that is becoming steeper
        2. observing the movement of the gondola on the left
        3. reading the values of the table on the right
        4. previous knowledge in physics about falling objects

        Since the gondola is constantly accelarating, what
        can you conclude about when it reaches its top speed?

The average speed is calculated by dividing the distance by the 
time:
$v_avg = \frac{\mbox{Height at beginning}  - \mbox{Height at end}}{\mbox{time needed for the path}}$, so in this case: $v_avg = \frac{70 m - 0 m}{4s}$

You can see that the gondola is accelerating from

        1. the slope of the graph that is becoming steeper
        2. observing the movement of the gondola on the left
        3. reading the values of the table on the right
        4. previous knowledge in physics about falling objects

        Since the gondola is constantly accelerating, it reaches
        its top speed at the end of the path, right before
        the brakes set in.

A = Point(xAxis)
B = Point(xAxis)
C = (-1, 75)
D = (-1.2, 75)
Vieleck1, a_1, b, c, d = Polygon(A, B, C, D)
f = If(x ≥ 0.0, If[x ≤ 4.0, -(70.0 / 16.0) * (x + 4.0) * (x - 4.0)])
t = 0 (slider from 0 to 4, step 0.01)
E: (t, f(t))
a = false
s: a ∧ t < 4.0
A5 = 0
A6 = 1
A7 = 2
A8 = 3
A9 = 4
B5 = 70
B6 = If(t ≥ 1.0, f(1.0))
B7 = If(t ≥ 2.0, f(2.0))
B8 = If(t ≥ 3.0, f(3.0))
B9 = If(t ≥ 4.0, f(4.0))
C6: B5 - B6
C7: B6 - B7
C8: B7 - B8
C9: B8 - B9
hint1 = false
solutions = false
hint2 = false
e = OrthogonalLine(E, yAxis)
g = OrthogonalLine(E, xAxis)
G = Intersect(g, xAxis)
i = Segment(E, G)
j = LineBisector(c)
H = Intersect(e, j)
h = Segment(E, H)
Vieleck2, k, l, m, n = Polygon((-(1.46), f(t)), (-(0.74), f(t)), (-(0.74), f(t) + 3.0), (-(1.46), f(t) + 3.0))