Final answer:
The gravitational potential energy of the cow at the top of the castle is 9,926.8 J, the elastic spring energy before release is 1,375 J, and the cow's speed right before landing is approximately 15.7 m/s.
Step-by-step explanation:
In the comedic context of Monty Python and the Holy Grail, we can apply principles of physics to a cinematic scenario. Given the specifications, we can calculate the gravitational potential energy (GPE), elastic spring energy (ESE), and speed upon impact for the catapulted cow.
Calculations:
- (a) To find the GPE at the top of the castle, we use the formula GPE = mgh, where m is the mass, g is the acceleration due to gravity (approximated as 9.8 m/s2), and h is the height. Plugging in the given values: GPE = 110 kg * 9.8 m/s2 * 9.1 m, we get GPE = 9,926.8 J (joules).
- (b) The ESE before the catapult is released can be determined by the formula ESE = 1/2 kx2, where k is the spring constant and x is the compression. So, ESE = 1/2 * 11000 N/m * (0.5 m)2, which equals ESE = 1,375 J.
- (c) To find the speed right before the cow lands, we must consider that the mechanical energy is conserved. The total energy (sum of GPE and ESE) at the start will be equal to the kinetic energy (KE) just before landing, which is KE = 1/2 mv2. Since GPE is zero at ground level, KE = initial GPE + ESE. Plugging in the values: 1/2 * 110 kg * v2 = 9,926.8 J + 1,375 J. Solving for v gives us a speed of approximately 15.7 m/s.