Final answer:
The correct answer is option C) 4.50 m/s.
Step-by-step explanation:
To determine the minimum speed that an athlete must leave the ground with to lift their center of mass 1.95 m and cross the bar with a speed of 0.60 m/s, we can use the principle of conservation of mechanical energy. At the highest point of the jump, the athlete's kinetic energy is zero and all of the initial mechanical energy is in the form of potential energy:
mg∆h = (1/2)mv²,
where m is the mass of the athlete, g is the gravitational acceleration (9.8 m/s²), ∆h is the vertical distance traveled, and v is the minimum speed required to achieve the desired final speed. Rearranging the equation and substituting the given values:
(63.0 kg)(9.8 m/s²)(1.95 m) = (1/2)(63.0 kg)v²,
Simplifying, we find:
v = √[(2 × 63.0 kg × 9.8 m/s² × 1.95 m) / 63.0 kg] = 4.50 m/s.
Therefore, the minimum speed the athlete must leave the ground with is 4.50 m/s.