Final answer:
The mechanical energy of the 59 kg student at the top of her high jump is approximately 1000 J, calculated by summing her kinetic and potential energy at that point.
Step-by-step explanation:
To calculate the mechanical energy of the student, we need to find the sum of her kinetic energy (KE) and potential energy (PE) at the top of her jump.
The kinetic energy (KE) of an object is given by the equation KE = ½mv², where m is mass and v is velocity. The potential energy (PE) due to gravity is given by the equation PE = mgh, where g is the acceleration due to gravity and h is the height above the ground.
For the 59 kg student with a speed of 2.9 m/s at 1.3 m above the ground, KE would be ½ * 59 kg * (2.9 m/s)², and PE would be 59 kg * 9.8 m/s² * 1.3 m.
Now, we calculate KE: KE = ½ * 59 kg * (2.9 m/s)² = 0.5 * 59 * 8.41 = 248.295 kg m²/s²
And then PE: PE = 59 kg * 9.8 m/s² * 1.3 m = 752.86 kg m²/s²
Adding both KE and PE to find the total mechanical energy gives us: Mechanical Energy = KE + PE = 248.295 kg m²/s² + 752.86 kg m²/s² = 1001.155 kg m²/s²
Rounding to the nearest hundred, we get a mechanical energy of approximately 1000 J (Joules).