Worked example 2.3: The Brooklyn bridge

Question: In 1886, Steve Brodie achieved notoriety by allegedly jumping off the recently completed Brooklyn bridge, for a bet, and surviving. Given that the bridge rises 135ft over the East River, how long would Mr. Brodie have been in the air, and with what speed would he have struck the water? Give all answers in mks units. You may neglect air resistance.
 
Answer: Mr. Brodie's net vertical displacement was $h = -135\times 0.3048 = -41.15 {\rm m}$. Assuming that his initial velocity was zero,

$$h = -\frac{1}{2} g t^2,$$

where $t$ was his time of flight. Hence,

$$t = \sqrt{\frac{-2 h}{g}} = \sqrt{\frac{2\times 41.15}{9.81}} = 2.896 {\rm s}.$$

His final velocity was

$$v =- g t = -9.81\times 2.896 = -28.41 {\rm m s}^{-1}.$$

Thus, the speed with which he plunged into the East River was $28.41 {\rm m s}^{-1}$, or $63.6 {\rm mi/h}$! Clearly, Mr. Brodie's story should be taken with a pinch of salt.