Certain insects can achieve seemingly impossible accelerations while jumping. the click beetle accelerates at an astonishing 400g over a distance of 0.52 cm as it rapidly bends its thorax, making the "click" that gives it its name. part a assuming the beetle jumps straight up, at what speed does it leave the ground? part b how much time is required for the beetle to reach this speed? part c ignoring air resistance, how high would it go?

(a) The beetle starts from rest and accelerates with an upward acceleration of 400 g and reaches its launching speed in a distance 0.53 cm. Here g is the acceleration due to gravity.

Use the equation of motion,

[tex]v^2=u^2+2as[/tex]

Here, the initial velocity of the beetle is u, its final velocity is v, the acceleration of the beetle is a, and the beetle accelerates over a distance s.

Substitute 0 m/s for u, 400 g for a, 9.8 m/s² for g and 0.52×10⁻²m for s.

[tex]v^2=u^2+2as\\ = (0 m/s)^2+2 (400)(9.8 m/s^2)(0.52*10^-^2 m)\\ =40.768 (m/s)^2\\ v=6.385 m/s[/tex]

The launching speed of the beetle is 6.4 m/s.

(b) To determine the time t taken by the beetle for launching itself upwards is determined by using the equation of motion,

[tex]v=u+at[/tex]

Substitute 0 m/s for u, 400 g for a, 9.8 m/s² for g and 6.385 m/s for v.

[tex]v=u+at\\ 6.385 m/s = (0 m/s) +400(9.8 m/s^2)t\\ t = \frac{6.385 m/s}{3920 m/s^2} = 1.63*10^-^3s=1.63 ms[/tex]

The time taken by the beetle to launch itself upwards is 1.62 ms.

(c) After the beetle launches itself upwards, it is acted upon by the earth's gravitational force, which pulls it downwards towards the earth with an acceleration equal to the acceleration due to gravity g. Its velocity reduces and when it reaches the maximum height in its path upwards, its final velocity becomes equal to zero.

Use the equation of motion,

[tex]v^2=u^2+2as[/tex]

Substitute 6.385 m/s for u, -9.8 m/s² for g and 0 m/s for v.

[tex]v^2=u^2+2as\\ (0m/s)^2=(6.385 m/s)^2+2(-9.8m/s^2)s\\ s=\frac{(6.385 m/s)^2}{2(9.8m/s^2)} =2.08 m[/tex]

The beetle can jump to a height of 2.1 m

okpalawalter8 okpalawalter8 · Answer 2 · 2022-02-01T15:23:06+01:00

We have that for the Question the Speed,Time and Height are

u=6.38m/s
T=13sec
h=2m

From the question we are told

Certain insects can achieve seemingly impossible accelerations while jumping.

the click beetle accelerates at an astonishing 400g over a distance of 0.52 cm as it rapidly bends its thorax, making the "click" that gives it its name.

Speed,Time and Height

a)

Generally the equation for the average velocity is mathematically given as

[tex]v^2-u^2=-2ah\\\\Therefore\\\\u=\sqrt{2*400*9.8*0.0052}\\\\[/tex]

u=6.38m/s

b)

Generally the equation for the Time of flight is mathematically given as

[tex]T=\frac{2u}{g}\\\\Therefore\\\\T=\frac{2(6.38)}{9.8}[/tex]

T=13sec

c)

Generally the equation for the air resistance is mathematically given as

[tex]v^2-u^2=2gh\\\\Therefore\\\\h=\frac{6.38^2}{2*9.8}\\\[/tex]

h=2m

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