AThe answer is 11.53 m/s
The final kinetic energy (KEf) is the sum of initial kinetic energy (KEi) and initial potential energy (PEi).
KEf = KEi + PEi
Kinetic energy depends on mass (m) and velocity (v)
KEf = 1/2 m vf²
KEi = 1/2 m vi²
Potential energy depends on mass (m), acceleration (a), and height (h):
PEi = m a h
So:
KEf = KEi + PEi
1/2 m vf² = 1/2 m vi² + m a h
..
Divide all sides by m:
1/2 vf² = 1/2 vi² + a h
We know:
vi = 9.87 m/s
a = 9.8 m/s²
h = 1.81 m
1/2 vf² = 1/2 9.87² + 9.8 1.81
1/2 vf² = 48.71 + 17.74
1/2 vf² = 66.45
vf² = 66.45 2
vf² = 132.9
vf = √132.9
vf = 11.53 m/s
b) The answer is 6.78 m
The kinetic energy at the bottom (KE) is equal to the potential energy at the highest point (PE)
KE = PE
Kinetic energy depends on mass (m) and velocity (v)
KE = 1/2 m v²
Potential energy depends on mass (m), acceleration (a), and height (h):
PE = m a h
KE = PE
1/2 m v² = m a h
Divide both sides by m:
1/2 v² = a h
v = 11.53 m/s
a = 9.8 m/s²
h = ?
1/2 11.53² = 9.8 h
1/2 132.94 = 9.8 h
66.47 = 9.8 * h
h = 66.47 / 9.8
h = 6.78 m
