Grasshoppers jump to avoid predators. They are programmed through natural select

Question

Grasshoppers jump to avoid predators. They are programmed through natural selection to optimize their trajectory by jumping rapidly at a 45 degree angle. The launch speed attained is 2.9 m/s for grasshopper with a mass of 2 g. The rear legs seem quite strong as seen in the plot below of force (F0=8 N) evolved over time after electrostimulating the rear leg muscle of a grasshopper (From W.J. Heitler's website, http://www.st-andrews.ac.uk/~wjh/jumping).

What momentum change needs to be provided by the leg muscle? (in N*s)

Examine the graph carefully, and from the plot, calculate how long after initiating a jump (the first blue point on the graph) will sufficient impulse be transferred to the grasshopper that it reaches the launch speed (choose the closest value that is within 10% of your calculated value). (in s)

Explanation / Answer

momentum = mv = 0.002 kg * 2.9 m/s = 0.0058 Ns

Now we have to calculate the time requiired to achieve this impulse by calculating the area under curve. Let it be t s

0.5 * t * 0.7Fo t /0.100 = 0.014 s

Hence time to achieve required momentum is 0.014 s

t^2 = 0.0058/[5*0.7*8] = 0.000207

t = 0.014 sec

Yes, the legs can provide this momentum

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