Explanation:
For each point:
PE = mgh
KE = ½ mv²
ME = PE + KE
Since energy is conserved, ME will be constant.
I'll be using g = 10 m/s².
A. PE = (100 kg) (10 m/s²) (102 m) = 102,000 J
KE = ½ (100 kg) (0 m/s)² = 0 J
ME = 102,000 J
B. KE = ½ mv²
18,000 J = ½ (100 kg) v²
v = 60 m/s
ME = 102,000 J
PE = ME − KE = 84,000 J
(100 kg) (10 m/s²) h = 84,000 J
h = 84 m
C. KE = ½ (100 kg) (29 m/s)² = 42,050 J
ME = 102,000 J
PE = ME − KE = 59950 J
(100 kg) (10 m/s²) h = 59950 J
h = 59.95 m
d. PE = (100 kg) (10 m/s²) (60 m) = 60,000 J
ME = 102,000 J
KE = ME − PE = 42,000 J
½ (100 kg) v² = 42,000 J
v = 29.0 m/s
E. PE = (100 kg) (10 m/s²) (0 m) = 0 J
ME = 102,000 J
KE = ME − PE = 102,000 J
½ (100 kg) v² = 102,000 J
v = 45.2 m/s
