MCQ Question related to trajectory of two projectiles

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The discussion revolves around determining the relationships between the time periods (T1, T2) and speeds (U1, U2) of two projectiles based on their trajectories. The user believes options A (T2 > T1) and D (U1 < U2) are correct but lacks confidence in their reasoning. They applied the formula "2uSin(theta)/g" to analyze the situation but are uncertain about the values used for U1 and U2. Another participant suggests focusing on the vertical component of projectile velocity and considering energy conservation principles for a clearer understanding. The conversation emphasizes the need for a solid rationale behind the chosen answers.
dahano
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Homework Statement

:
The trajectort of two projectiles are shown in the figure. Let T1 & T2 be the rime periods and U1 and U2 be their speeds of projection. Then(state the answer with REASON):

A) T2 > T1
B) T1 = T2
C) U1 > U2
D) U1 < U2

image.png
[/B]

(MAYBE, MORE THAN ONE CORRECT)

Homework Equations

: 2D Motion/kinematics.[/B]

The Attempt at a Solution

: I feel that the option A & D should be correct but I'm not quite sure and neither I've a proper reason for it. btw, I've used "2uSin(theta)/g" to figure out that A & D are the answer but I'm not sure.[/B]
 
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dahano said:
I feel that the option A & D should be correct but I'm not quite sure and neither I've a proper reason for it. btw, I've used "2uSin(theta)/g" to figure out that A & D are the answer but I'm not sure.

What makes you feel this ?
 
Qwertywerty said:
What makes you feel this ?
I used "2uSin(theta)/g" but the values that I put for "u" were like u2 > u1. And this is why I'm not sure of my answer and I doubt that it may be wrong.
 
dahano said:
I used "2uSin(theta)/g" but the values that I put for "u" were like u2 > u1. And this is why I'm not sure of my answer and I doubt that it may be wrong.

What relation do you get from H1 = H2 ?
 
what does that expression tell us? uSin(theta) is simply the vertical component of the projectile velocity, so you might want to just focus on this fact and consider using the law of energy conservation to tackle the problem.
 
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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