Respuesta :
Let say the Fly jumps in the air with speed speed vertically upwards
[tex]v_y = v_0[/tex]
it will reach the highest point the final speed will become Zero
so here we can say that its uniform deceleration due to gravity of earth
[tex]v_f = 0[/tex]
[tex]a = - g[/tex]
now by kinematics we can say
[tex]v_f^2 - v_i^2 = 2 a d[/tex]
[tex]0 - v_0^2 = 2*(-g)*H[/tex]
[tex]H = \frac{v_0^2}{2g}[/tex]
so above is the maximum height that will covered by the fly.
The flea goes up to a height given by the equation [tex]\boxed{H = \frac{{v_f^2}}{{2g}}}[/tex].
Further Explanation:
Given:
The velocity of the flea on the ground i.e. the initial velocity is [tex]0\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}[/tex].
The flea jumps in the air in vertically upward direction.
Concept:
As the flea jumps in vertically upwards direction, it will move under the acceleration due to gravity. The motion of the flea is governed by the third equation of motion.
The third equation of motion can be written as.
[tex]v_f^2 = v_0^2 + 2gH[/tex]
Here, [tex]{v_f}[/tex] is the final velocity of the flea, [tex]{v_0}[/tex] is the initial velocity of the flea and [tex]H[/tex] is the height attained by the flea as it jumps.
Since the flea starts from rest, the initial velocity of the flea should be [tex]0\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}[/tex].
Substitute the values and rearrange the equation for [tex]H[/tex].
[tex]\begin{aligned}v_f^2 &= {\left( 0 \right)^2} + 2gH \hfill\\H&= \frac{{v_f^2}}{{2g}} \hfill\\\end{aligned}[/tex]
Thus, the flea goes up to a height given by the equation [tex]\boxed{H = \dfrac{{v_f^2}}{{2g}}}[/tex].
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Answer Details:
Grade: High School
Chapter: Kinematics
Subject: Physics
Keywords: Flea jumps, vertically up, no air resistance, neglect, initial velocity, final velocity, acceleration, height, equation of motion.
