An average froghopper insert has a mass of 12.4 mg and jumps to a maximum height

Question

An average froghopper insert has a mass of 12.4 mg and jumps to a maximum height of 278 mm when its takeoff angle is 62.0 degrees above the horizontal.

a.) Find the takeoff speed of the froghopper.

b.) How much kinetic energy did the froghopper generate for this jump? Express your answer in microjoules.

c.) How much energy per unit body mass was required for the jump? Express your answer in joules per kilogram of body mass.

An average froghopper insect has a mass of 12.4 mg and jumps to a maximum height of 278 mm when its takeoff angle is 62.0° above the horizontal. Find the takeoff speed of the froghopper takedffangle is 62.0' above the horizontal. Find the Number m/s How much kinetic energy did the froghopper generate for this jump? Express your answer in microjoules. Number How much energy per unit body mass was required for the jump? Express your answer in joules per kilogram of body mass. Number J/kg

Explanation / Answer

part a

by the kinematics equation

vf2 = vi2 + 2gh

here direction of accelartion is opposite of displacement so g is negaitve

and final speed is zero till reach height h

let take off speed is V

Vsin62 =vi

0 = vi2 -2*9.81*0.278

vi = 2.335457 m

take of velocity V= vi/ sin62 = 2.64506 m/s

part b

kinetic energy = change in potential energy = mgh=12.4*10-3*9.81*0.278 = 3.3817*10-2 J or 0.5mvi2

value coame out same

part c

energy perunit body = 3.3817*10-2/12.4*10-3 = 2.7272J/Kg

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