Maddie is standing still when her dancing partner begins to lift her up and thro

Question

Maddie is standing still when her dancing partner begins to lift her up and throws her into the air. Maddie's mass is 40 kg and her partner exerts an average vertical force of 500 N for 1.0 s on Maddie during the lift and throwing motion.

a) What is Maddie's vertical velocity when her partner releases her?

using the impulse momentum I get 12.5 m/s. this does not agree with the answer of 2.69 m/s upward. how did they get there?

b) If Maddie's center of gravity was 1.5 m above the floor when released , what height will she reach?

Explanation / Answer

12.5 m/s would be if the push were not against the force of gravity. We need to find the net force on Maddie. F up - mg = net force 500N up - 40kg*9.81m/s^2 down = 107.6 N up F = ma F/m = a = 107.6N/40kg = 2.69 m/s^2 If you accelerate at 2.69 m/s^2 for one second your speed is 2.69 m/s b) position = starting position + vt - 1/2 g t^2 no, we don't have time final velocity squared = starting velocity squared - 2 g change in height or we could use kinetic energy turns to potential energy 1/2 m v^2 = m g h (1/2) v^2 / g = h (1/2)*(2.69m/s)^2/9.81 m/s^2 = 0.369 m above her starting point 1.5 + 0.369 = 1.87 m

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