A ball of mass 8 kg falls from rest from a height of 100 m
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Step-by-step solution
3 stepsHere's how to calculate the kinetic energy of the ball just before it hits the ground.
Formula:
The kinetic energy (KE) of an object is given by the formula:
KE = (1/2) × mass × velocity²
To use this formula, we first need to find the velocity of the ball just before it hits the ground. We can use the following kinematic equation:
v² = u² + 2as
where:
v = final velocity
u = initial velocity
a = acceleration (due to gravity, g ≈ 9.8 m/s²)
s = distance (height)
Calculate the final velocity (v).
The ball falls from rest, so its initial velocity (u) is 0 m/s.
The acceleration (a) is the acceleration due to gravity, g = 9.8 m/s².
The distance (s) is the height, 100 m.v² = (0 m/s)² + 2 × (9.8 m/s²) × (100 m)
v² = 0 + 1960 m²/s²
v² = 1960 m²/s²Calculate the kinetic energy (KE).
Now we can substitute the value of v² into the kinetic energy formula.
Mass (m) = 8 kg.KE = (1/2) × m × v²
KE = (1/2) × (8 kg) × (1960 m²/s²)
KE = 4 kg × 1960 m²/s²
KE = 7840 kg·m²/s²State the final answer with the correct units.
The unit kg·m²/s² is equivalent to Joules (J), the SI unit for energy.
The kinetic energy of the ball just before it hits the ground is 7840 J.
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