Superwoman is hovering above the ground when a person free-falling goes by her at a terminal velocity of 140 km/h. Unfortunately, the parachute does not open. Fortunately, Superwoman is around. If it takes her 1.9 s to realize the person is in distress, what must her acceleration bee if she is to catch the parachutist just before she hits the ground 1000 m below?
Well, it seems like Superwoman has her work cut out for her! She needs to catch the falling parachutist just before they hit the ground. Now, before we calculate her required acceleration, let me tell you a little joke to lighten the mood.
Why don't scientists trust atoms?
Because they make up everything!
Now that we have a smile on our faces, let's get back to the calculations. We can use the equation of motion to find Superwoman's required acceleration. The equation is:
s = ut + (1/2)at^2
Where:
s = distance traveled (1000 m)
u = initial velocity of the falling person (140 km/h)
t = time taken for Superwoman to react (1.9 s)
a = required acceleration
First, let's convert the initial velocity into meters per second:
140 km/h = (140 * 1000 m) / (60 * 60 s) ≈ 38.9 m/s
Now, we can plug the values into the equation and solve for the acceleration:
1000 = (38.9 * 1.9) + (1/2) * a * (1.9)^2
After some calculations, we find that the required acceleration for Superwoman to catch the parachutist just before they hit the ground is approximately 39.5 m/s².
So, Superwoman needs to accelerate at a rate of 39.5 m/s² to save the day! Just remember, not all heroes wear capes, some wear clown noses and crack jokes.
To find the required acceleration of Superwoman, we need to calculate the time it takes for the person to hit the ground and then determine the acceleration needed to cover that distance in the given time.
Let's start by finding the time it takes for the person to reach the ground using the equation for free fall:
d = (1/2) * g * t^2
where:
d = distance = 1000 m
g = acceleration due to gravity = 9.8 m/s^2
t = time
Rearranging the equation, we get:
t^2 = (2 * d) / g
t^2 = (2 * 1000) / 9.8
t^2 ≈ 204.08
t ≈ √204.08
t ≈ 14.28 s
Now, we know that the time Superwoman has to catch the person is 1.9 s. Therefore, her acceleration needs to be high enough to cover the remaining distance in this time:
d = (1/2) * a * t^2
where:
d = remaining distance = 1000 m
a = acceleration (to be determined)
t = time = 1.9 s
Substituting the values into the equation, we get:
1000 = (1/2) * a * (1.9^2)
Simplifying further:
2000 = a * 3.61
a = 2000 / 3.61
a ≈ 553.46 m/s^2
Therefore, Superwoman must accelerate at approximately 553.46 m/s^2 to catch the parachutist just before she hits the ground.