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jiteshmeghwal9
 one year ago
A grasshopper can jump a maximum horizontal distance of 40cm. If it spends negligible time on the ground then in this case its speed along horizontal road will be
jiteshmeghwal9
 one year ago
A grasshopper can jump a maximum horizontal distance of 40cm. If it spends negligible time on the ground then in this case its speed along horizontal road will be

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Considering that the grasshopper starts on the ground and lands on the ground, there is no change in elevation. The range of the grasshopper is given by: \[R=\frac{v^{2}\sin 2\theta }{g}\] If we now take the information that this is a maximal distance, the maximum range is given when the angle of launch is 45 degrees. This yields the equation: \[R_{max}=\frac{v^{2}}{g}\] We know R_max=0.4 m and g=9.8 m/s^2, so we can solve for v: \[v=1.98 m/s\] We are asked for the horizontal component, which by trigonometry is: \[v_{x}=v\cos\theta \] We again take our angle of launch as 45 degrees and arrive at: \[v_{x}=1.40 m/s \]
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