Really with projectice problems

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The discussion revolves around solving projectile motion problems involving a water balloon, a baseball throw, and a rocket launch. The water balloon is thrown from a height of 25m at a speed of 20m/s and strikes another building 20m away at a height of 6.9m. The third baseman throws a ball horizontally from 3ft above ground, and it lands 73ft from first base. The rocket is launched at an angle of 70 degrees with an acceleration of 46 m/s², achieving a flight time of 309 seconds, a maximum height of 10,500m, and impacting the ground at a velocity of 1513 m/s at an angle of -72 degrees. Participants emphasize the importance of showing work to identify errors in calculations.
Petrikovski
A water balloon is thrown at 20m/s from the roof of a building 25m high at an angle of 30 degrees below horizontal. At what height above ground wil alloon strike side of another building 20m away from first? 6.9m

A third baseman wishes to throw to first bas, 127 ft distant. His best trhrowing speed is 85 m/hr (g = -32 ft/s). If he throws horizontally 3 ft above the ground, how far from first base will it hit the ground? (1 mi/hr = 1.467 ft/s) 73 ft

and

A rocket is launched form rest and moves in a straight line at 70 degrees above the horizontal with an accel of 46 m/s^2. After 30 s the engines shut off and the rocket free-falls back to Earth in a parabolic path. Assume no air resistance.
Find the time of flight. 309s
What is max height. 10500 m
What is distance from launch pad to impact point? 13900
What velocity does rocket hit ground with? 1513 m/s @ -72 degrees

ive tried them all and i just can't get the right answer. this is driving me crazy
 
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It will be easier to find where you have gone wrong if you show us what you have done.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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