1. Typical data for an expert pole-vaulter gives their horizontal component of velocity as 8 m/s and their vertical component as 2 m/s at take-o'. (a) If someone simply jumped at the vertical component of the velocity, how high could they get? (b) How does a pole-vaulter convert all (or at least most) of the horizontal component of velocity to \"vertical\" energy (i.e., gravitational potential energy)? [Hintz See the picture below.] (c) If all of the pole-vaulter's kinetic energy was directly converted to gravitational potential energy, how high could the pole-vaulter's centre-of-mass rise (d) Is this enough for success as a world-class pole-vaulter'? (The world standards are around 6 m for men and 5 m for women.) (e) What velocity would be needed to reach world standards for men and for women? 2. To demonstrate the power (no pun intended) of using energy conservation in solving problems, let's revisit the Activity 3: Question 4 of the week 6 workshop in which the fall height was determined that would result in a man breaking his leg if the thighbone absorbed the entire force of impact. In that question, the maximum applied force of compression of one man's thighbone can endure without breaking is 7.0 x 104 N. The maximum effective cross-sectional area of the bone is 4.0 x 104m2, its length is 0.55 m, andYoung' s modulus is 9. 4 x 109N/m2. The mass ofthe manis 65 kg. Based on this maximum applied force of compression, a change of length of AL: 0. 01 m was determined for the thighbone just before breaking. (a) Assuming the thighbone is an elastic material, what is the work needed to compress the thighbone by AL = 0.01 m? (b) Assuming the man falls and the change in gravitational potential energy goes entirely into work to compress the thighbone, what is the maximum height that the man's centre of mass can fall under gravity without breaking his thighbone