On a dare, you decide to try bungee jumping. You fall freely you are moving at 15 m/s downward. At that point the cord begins to stretch. The cord slows you to a stop as it stretches, then pulls you back upwards. When the cord is no longer pulling on you, you are moving upwards at 8 m/s. The time between moving at 15 m/s downward and moving 8 m/s upward is 3 seconds. Draw a motion diagram for this situation. What is your acceleration as the bungee cord changes your direction? What is the direction of that acceleration?
To draw a motion diagram for this situation, we can break down the motion into different intervals:
1. From the starting point to the point where the cord starts to stretch: Draw an arrow pointing downwards to represent your initial motion at 15 m/s.
2. From the point where the cord starts to stretch to the point where you reach the peak downward speed: Draw a downward arrow that gradually becomes shorter to represent the slowing down of your motion.
3. At the point of zero speed and the direction starts to change: Draw a dot to represent the momentary stop in your motion.
4. From the point of zero speed to the point of maximum upward speed: Draw an upward arrow that gradually becomes longer to represent your acceleration in the opposite direction.
5. From the point of maximum upward speed to the point where you stop moving upwards: Draw an upwards arrow that gradually becomes shorter to represent the slowing down of your motion.
Considering the information given and the motion diagram, we can calculate the acceleration as follows:
Using the equation of motion, v = u + at, where:
- v is the final velocity,
- u is the initial velocity,
- a is the acceleration, and
- t is the time.
For the first interval, from 15 m/s downwards to 0 m/s, the time taken is 3 seconds.
Using the equation, 0 (final velocity) = 15 (initial velocity) + a (acceleration) * 3 (time),
we can solve for acceleration: a = -5 m/s².
For the second interval, from 0 m/s to 8 m/s upwards, the time taken is also 3 seconds.
Using the equation, 8 (final velocity) = 0 (initial velocity) + a (acceleration) * 3 (time),
we can solve for acceleration: a = 8/3 m/s².
Therefore, the acceleration as the bungee cord changes your direction is:
-5 m/s² during the downward phase and 8/3 m/s² during the upward phase.
The direction of acceleration:
- During the downward phase, the acceleration is in the opposite direction of motion, i.e., upwards.
- During the upward phase, the acceleration is in the same direction as motion, i.e., upwards.