How tall is a building if a woman falls for 2.30 seconds before being caught by Superman?

To determine the height from which the woman falls for 2.30 seconds under the influence of gravity, we can use the kinematic equation for uniformly accelerated motion. The relevant equation here is:

[

d = v_i t + \frac{1}{2} a t^2

]

In this case, the initial velocity ((v_i)) is zero because the woman starts from rest, and the acceleration ((a)) is approximately (9.81 , m/s^2) (the acceleration due to gravity).

Plugging in the values:

1. The time ((t)) is (2.30) seconds.

2. The expression simplifies to:

[

d = 0 \cdot t + \frac{1}{2} (9.81) (2.30)^2

]

Calculating this step-by-step:

• First calculate ( (2.30)^2 = 5.29 ).

• Then calculate ( \frac{1}{2} \times 9.81 \times 5.29 ).

This yields:

[

d = \frac{1}{2} \times 9.81 \times 5.29