Final answer:
A bungee jumper dropping from a 50.0m height with no air resistance would take approximately 3.19 seconds to reach the ground.
Step-by-step explanation:
To calculate how long it would take for a bungee jumper to drop straight down from a height of 50.0m without air resistance, we use the formula for the time of free fall under the constant acceleration due to gravity. The formula is derived from the equation of motion under constant acceleration, which is:
s = ut + ½at²
where:
- s is the distance fallen (50.0m)
- u is the initial velocity (0 m/s, as the jumper starts from rest)
- a is the acceleration due to gravity (9.80 m/s²)
- ½ is a constant fraction
- t is the time in seconds
Since the initial velocity, u, is 0 m/s, our formula simplifies to:
s = ½at²
By rearranging the formula to solve for time, t, we get:
t = sqrt(2s/a)
We can now plug in the values:
t = sqrt(2 * 50.0m / 9.80 m/s²) = sqrt(10.20408) ≈ 3.19 seconds
Therefore, it would take the bungee jumper approximately 3.19 seconds to drop from a height of 50.0m, assuming no air resistance.