Would you mind checking one of my problems from my physics study guide? I know the answer and just want to make sure I am using the right formula. :)

A 78-kg skydiver has a speed of 62 m/s at an altitude of 870 m above the ground.
a. Determine the kinetic energy possessed by the skydiver. (149916 J)

Formula: K.E=1/2mv2
b. Determine the potential energy possessed by the skydiver. (665028 J)

Formula: P.E=mgh
c. Determine the total mechanical energy possessed by the skydiver. (814944 J)

Formula: M.E=K.E + P.E

To confirm whether you are using the right formulas, let's go through each part step by step:

a. To determine the kinetic energy (K.E) possessed by the skydiver, you are correct in using the formula K.E = (1/2)mv^2, where m is the mass of the skydiver and v is the speed. In this case, the mass of the skydiver is given as 78 kg, and the speed is given as 62 m/s. Substituting these values into the formula, we have:
K.E = (1/2)(78 kg)(62 m/s)^2 = 149,916 J

So your answer of 149,916 J is correct.

b. To determine the potential energy (P.E) possessed by the skydiver, you should use the formula P.E = mgh, where m is the mass of the skydiver, g is the acceleration due to gravity, and h is the height above the ground. In this case, the mass is 78 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height is 870 m. So, plugging in these values into the formula, we have:
P.E = (78 kg)(9.8 m/s^2)(870 m) = 665,028 J

Therefore, your answer of 665,028 J for the potential energy is correct.

c. To determine the total mechanical energy (M.E) possessed by the skydiver, you add the kinetic energy (K.E) and the potential energy (P.E). So, using the values we calculated earlier:
M.E = K.E + P.E = 149,916 J + 665,028 J = 814,944 J

Hence, your answer of 814,944 J for the total mechanical energy is also correct.

Congratulations on using the right formulas and getting the correct answers!