In an old science fiction movies, writers tried to come up with novel ways of launching spacecraft in the direction of the moon. In one hypothetical case, a screenwriter envisioned launching a moon probe from a deep, smooth tunnel, inclined at 73.0° over the horizontal. At bottom of the tunnel a very stiff spring designed to launch the craft was anchored. The top of the spring, when the spring is unstressed, is 32.0 m from the higher end of the tunnel. The screenwriter knew from his research that to arrive at the moon, the probe of 318 kg must have a speed of at least 11.2 km/s when it exits the tunnel. When the spring is compressed by 83.0 m just before launch, determine the minimum value for its force constant to accomplish a successful launch? Avoid friction with the tunnel walls and floor.