Agrasshopper 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

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

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.