A sky-diver steps out from a helicopter and falls 5s before reaching her terminal velocity of 50 mi/h. Her acceleration just before reaching terminal velocity is what?
zero
terminal velocity means constant speed down, no acceleration so approaching terminal velocity means approaching zero acceleration
To find the acceleration just before reaching terminal velocity, we need to use the equation of motion:
v = u + at
Where:
v = final velocity (terminal velocity)
u = initial velocity (0 mi/h as the skydiver steps out from the helicopter)
a = acceleration
t = time (5s before reaching terminal velocity)
Since the skydiver is falling, we can assume that the acceleration will be negative (opposite to the direction of motion).
Given:
v = 50 mi/h
u = 0 mi/h
t = 5s
Let's substitute the values into the equation and solve for acceleration (a):
50 = 0 + a * 5
50 = 5a
Dividing both sides by 5:
10 = a
Therefore, the acceleration just before reaching terminal velocity is -10 mi/h/s (negative because it is directed opposite to the motion).
To find the acceleration just before reaching terminal velocity, we need to use the formula for acceleration:
acceleration = change in velocity / time
In this case, the change in velocity would be the difference between the terminal velocity and the initial velocity, and the time would be the 5 seconds she falls before reaching terminal velocity.
The initial velocity is not mentioned, but we can assume it to be zero since the skydiver is stepping out from a helicopter and hasn't started falling yet.
So, the change in velocity would be:
change in velocity = terminal velocity - initial velocity
= 50 mi/h - 0 mi/h
= 50 mi/h
Now, let's calculate the acceleration:
acceleration = change in velocity / time
= 50 mi/h / 5 s
= 10 mi/(h*s)
Therefore, the acceleration just before reaching terminal velocity is 10 miles per hour per second (mi/h/s).