Grasshoppers are known to be very good jumpers. While they are about 5 centimeters long, they can make a standing long jump of about 1 meter, twenty times their length! While doing that, they reach a peak height of about 30 centimeters. Here we will try to estimate what forces they exert on the ground while jumping. Ignore air resistance throughout this problem. 1. Using the maximum height of the projectile trajectory to find the y- component of velocity when the grasshopper leaves the ground and the time of flight. 2. Using the range of the trajectory and the time of flight to find the x- component of velocity when the grasshopper leaves the ground. 3. Find the speed of the grasshopper when it leaves the ground. 4. The grasshopper acquires this speed by pushing on the ground. Draw the free-body diagram of the grasshopper just before take-off. 5. Slow-motion videos suggest that grasshoppers push the ground for about 15 milliseconds before take-off. Assuming the acceleration is constant throughout this time interval, estimate the acceleration of the grasshopper just before take-off and compare it to the acceleration due to gravity g.