In Mostar, Bosnia, the ultimate test of a
young man’s courage once was to jump off
a 400-year-old bridge (now destroyed) into
the River Neretva 24 m below the bridge.
How long did the jump last? The acceleration
of gravity is 9.8 m/s
2
.
Answer in units of s
24 = (1/2)g t^2
48 = 9.8 t^2
t 2.21 seconds
To calculate how long the jump lasted, we can use the kinematic equation for motion in a vertical direction:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- s is the vertical displacement (in this case, 24 meters).
- u is the initial velocity (which is zero since the person starts from rest).
- a is the acceleration due to gravity (which is -9.8 m/s^2, considering it acts in the opposite direction of motion due to downward motion).
- t is the time taken.
Rearranging the equation to solve for t, we get:
\[ t = \sqrt{\frac{2s}{a}} \]
Substituting the given values:
\[ t = \sqrt{\frac{2 \cdot 24}{-9.8}} \]
Calculating this expression:
\[ t \approx 2.78 \, \text{s} \]
Therefore, the jump lasted approximately 2.78 seconds.