Maddie is standing still when her dancing partner, Paul, begins to lift her up and throw her into the air. Maddie’s mass is 40 kg. Paul exerts an average vertical force of 500 N for 1.0 s on Maddie during the lift and throwing motion. What is Maddie’s vertical velocity when Paul releases her?

So far I have a=F/m
a=500N/40kg
a=12.5m/s^2
However since you're working against gravity I have 12.5-9.81= 2.69m/s2

Well, well, well, Maddie is in for a gravity-defying adventure, isn't she? Now, let's see if we can calculate her vertical velocity as the fearless Paul releases her into the air.

You're off to a great start with calculating the acceleration, given by a = F/m. Using your numbers, aahh, er... I mean, using the correct numbers: a = 500N / 40kg = 12.5 m/s^2.

But hold that laughter (or scream) for a moment! You are correct that we need to consider the force of gravity, my friend. You subtracted 9.81 m/s^2 from 12.5 m/s^2, giving you a net acceleration of 2.69 m/s^2. Well done!

Now, we need to determine Maddie's velocity when Paul releases her. Thankfully, we have a sneaky little formula for that: v = u + at, where u is the initial velocity (which we'll assume is zero because Maddie was standing still) and t is the time (which is given as 1.0 second).

Plug those values in, my friend! Let the calculations begin! v = 0 + (2.69 m/s^2 * 1.0 s) = 2.69 m/s.

There you have it, Maddie's vertical velocity when Paul releases her is 2.69 m/s. She's truly flying high! But remember, gravity is always watching, ready to pull her back down. Gravity is such a party pooper.

To find Maddie's vertical velocity when Paul releases her, you need to calculate the change in velocity during the time Paul exerts the force on her.

Step 1: Calculate the acceleration:
The acceleration can be found using the formula:
a = F / m
where a is the acceleration, F is the force, and m is the mass.

Given that the force exerted by Paul is 500 N and Maddie's mass is 40 kg, you have:
a = 500 N / 40 kg
a = 12.5 m/s^2

Step 2: Subtract the gravitational acceleration:
Since Maddie is being lifted upwards against the force of gravity, you'll need to subtract the gravitational acceleration from the calculated acceleration. The acceleration due to gravity is approximately 9.81 m/s^2.

So, the net acceleration is:
a_net = a - g
a_net = 12.5 m/s^2 - 9.81 m/s^2
a_net = 2.69 m/s^2 (rounded to two decimal places)

Step 3: Calculate the vertical velocity:
Using the formula for calculating velocity, which relates initial velocity, acceleration, and time:
v = u + at

Assuming Maddie starts from rest and the time Paul exerts the force is 1.0 s, the equation becomes:
v = 0 + (2.69 m/s^2) * 1.0 s
v = 2.69 m/s

Therefore, Maddie's vertical velocity when Paul releases her is 2.69 m/s

To calculate Maddie's vertical velocity when Paul releases her, you can use the concept of acceleration and the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

In this case, Maddie starts from rest (u = 0) and experiences an acceleration of 2.69 m/s² for a duration of 1.0 second. Therefore, you can calculate Maddie's final vertical velocity as follows:

v = u + at
v = 0 + (2.69 m/s²)(1.0 s)
v = 2.69 m/s

So, Maddie's vertical velocity when Paul releases her is 2.69 m/s.

so what is her vertical velocity after one second?

you found the correct acceleration