## 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

1. jiteshmeghwal9

@UnkleRhaukus

2. jiteshmeghwal9

@ganeshie8

3. anonymous

Considering 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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