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.

In a steady-flow steam power plant system, two adiabatic high-pressure and low-pressure turbines ane used to generate power. superheated steam enters the high-pressure turbine at 8 mpa and 550°c. the steam expands in the high-pressure turbine to a saturated vapor at 3 mpa. in order to increase the powe generation of the power plant, another steam turbine working in a lower pressure ranges is deployed. the outlet vapor from the first turbine is heated up at a boiler to the temperature of 500 c at the constant pressure of first turbine's outlet (3 mpa). then, the vapor enters the second turbine and produces extra work. the exit conditions of the second turbine are 5o kpa and 90 percent quality. if the total power output of the power plant is 25 mw, determine a) the mass flow rate of the water (kg/s). b) heat transfer rate in the boiler (mw). (30 points) 3 mpa 00 c 8 mpa s0 c high pres turbine low pres boiler turbine 50 kpa 3 mpa 09 saturated vapor t heat engine, shown in the figure, operates between high temperature and low temperature of through a heat 4. a carnot tn and tu respectively. this heat engine receives energy from a heat reservoir at t exchanger where the heat transferred is proportional to the temperature difference as ? = k (z,-7, ). it rejects heat at a given low temperature tl. to design the heat engine for maximum work output, find the high temperature, th, as a function of tes and t. (15 points) qe

Arod of some material 0.20 m long elongates 0.20 mm on heating from 21 to 120°c. determine the value of the linear coefficient of thermal expansion [in (degrees c)^-1] for this material.

Which statements describe the movement of ocean currents around the globe? check all that apply. strong winds force warm water to sink to the ocean floor. the coriolis effect causes warm and cold water to mix. cool dense water sinks to the ocean floor. warm water replaces cool surface water. wind blowing parallel to the shore causes upwelling of cool water.