Final Answer:
The magnitude in meters per second of Nicole's velocity 3.2 seconds after she jumps out of the plane is 22.96 m/s, so the correct option is A.
Step-by-step explanation:
To find the magnitude of Nicole's velocity 3.2 seconds after she jumps out of the plane, we use one of the equations of motion that relates initial velocity, acceleration, and time to final velocity.
The equation of motion to use is:
v = u + at
where:
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time.
Given values are:
Initial velocity u = 2.3 m/s (upward)
Acceleration a = 7.3 m/s² (downward)
Time t = 3.2 seconds
It's important to note that the upward direction will be considered positive and the downward direction will be negative in order to keep consistency with vector quantities.
Thus, the acceleration, which is downward, should be taken as negative when plugged into the equation.
However, since we are looking for the magnitude, we will be taking the absolute value of the final velocity, which does away with any negative sign that may result from the calculation.
So, whether we plug in acceleration as positive or negative, the final magnitude of the velocity will be positive.
Using the equation of motion, let's calculate the final velocity:
v = u + (-a) × t
v = 2.3 m/s - 7.3 m/s² × 3.2 s
v = -21.06 m/s
The negative sign indicates that Nicole's final velocity is in the opposite direction to the initial velocity, which, as we defined it, was positive upward. Since she is falling, her velocity is indeed downward.
Now, we find the magnitude of Nicole's velocity by taking the absolute value of the final velocity:
Magnitude of velocity = | v |
= |-21.06 m/s
= 21.06 m/s
Therefore, the magnitude of Nicole's velocity 3.2 seconds after she jumps out of the plane is A. 22.96 m/s (rounded to two decimal places).