Projectile Motion of a Grasshopper Problem

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Homework Help Overview

The problem involves a grasshopper leaping from the edge of a vertical cliff, requiring the determination of its initial speed and the height of the cliff based on provided information and equations of motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of kinematic equations and question the signs used for initial velocity and acceleration due to gravity. There is an exploration of the implications of negative values under radicals in calculations.

Discussion Status

Some participants have offered clarifications regarding the signs of the variables involved, particularly the treatment of gravity and initial velocity. Multiple interpretations of the equations are being explored, and there is an ongoing examination of the assumptions made in the calculations.

Contextual Notes

Participants are working with a diagram that is not visible in the thread, which may be affecting their understanding of the problem setup. There is also a mention of a negative value encountered in calculations, indicating potential missing information or misinterpretation of the problem's parameters.

maff is tuff
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Homework Statement



A grasshopper leaps into the air from the edge of a vertical cliff, as shown in the figure below.

Use information from the figure to find a) the initial speed of the grasshopper and b) the height of the cliff.

Homework Equations



v=v0 + at

x = x0 + v0t + 1/2(at^2)

v^2 = v0^2 + 2a(x-x0)

The Attempt at a Solution



I think I am missing something big because I'm not even getting close. I keep getting a negative under a radical. Can you please tell me what I am doing wrong or point me in the right direction? The diagram and my attempt is attached below. Thanks for the help:)

 

Attachments

  • Grasshopper Trajectory.jpg
    Grasshopper Trajectory.jpg
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  • grasshopper attempt.pdf
    grasshopper attempt.pdf
    131.1 KB · Views: 693
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You are right that voy =gt where t is the time the grasshopper reaches the maximum height. But you substituted -gt for voy in the equation for the displacement.

ehild
 
Doesn't gt have to be negative? Because gravity is downward and my initial velocity is upward so g has to be negative. right?
 
Gravity is negative, but g=9.8 m/s2, and the acceleration is -g. But voy is positive (upward) voy=gt=9.8t

ehild
 

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