To reach the top of the building, Batman's grappling hook needs to be traveling with a speed of 31.5 m/s when it leaves the barrel of his grappling gun. What must be the minimum spring constant of the grappling hook's spring in order to successfully reach this speed, ignoring the effects of friction as the hook travels through the barrel?b) If the spring constant of the grappling hook is actually a bit larger, k = 155 kN/m, to account for the effects of friction, how much thermal energy is absorbed by the grappling gun as the hook travels through the barrel?c) Using conservation of energy, how fast will the hook be moving when it hits the top of the building? 

 

Batman fires his grappling hook to reach the top of a building 23.2 m above his grappling gun, a horizontal distance of 27.2 m away. His grappling hook operates by firing the hook using a very stiff spring, which is compressed by 42.3 cm when the gun is loaded. He aims the gun upwards at 49.5 above the ground and fires the grappling hook. Ignore the effects of air resistance on the hook as it flies.