How do I calculate the time and distance for a pendulum projectile problem?

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To calculate the time and distance for a pendulum projectile problem, the formula d=vt is used to find distance in the x-plane. The user initially struggled to determine the time in seconds but eventually found it using the formula t=(2dy/g)^1/2. This formula calculates the time from release to landing based on the vertical displacement (dy) and gravitational acceleration (g). With the time determined, the distance can then be calculated effectively. Understanding these formulas is crucial for solving pendulum projectile problems accurately.
velocityoverrtime2
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Homework Statement
A mass has a maximum speed of 1.905 m/s when it is at the lowest point of a pendulum swing. The lowest point is 0.5984 meters off the floor. At which horizontal position on the floor from the pendulum equilibrium position must a target be placed to hit the center of the target?
Relevant Equations
mgh=1/2mv^2
d=vt
Tried to find time in seconds in order to use the formula d=vt and find the distance in the x plane in which the target must be placed, to no avail.
 
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velocityoverrtime2 said:
Nevermind I found time from release to landing by using the formula t=(2dy/g)^1/2
 
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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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