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=v2sin2θg
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: Rmax=v2g
We know R_max=0.4 m and g=9.8 m/s^2, so we can solve for v: v=1.98m/s
We are asked for the horizontal component, which by trigonometry is: vx=vcosθ
We again take our angle of launch as 45 degrees and arrive at: vx=1.40m/s
