To determine the speed of the body just before it strikes the ground, we can use the principle of conservation of energy. The potential energy at the initial height will be converted into kinetic energy at the final height.
The potential energy (PE) of an object at a height h is given by the formula:
PE = mgh
Where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height.
In this case, the potential energy at the initial height is:
PE_initial = mgh = (0.0045 kg)(9.8 m/s²)(10.5 m) = 0.45525 J
At the final height (the ground), all of the potential energy will be converted into kinetic energy (KE). The kinetic energy of an object is given by the formula:
KE = (1/2)mv²
Where m is the mass and v is the velocity (speed).
Setting the potential energy equal to the kinetic energy, we have:
PE_initial = KE_final
0.45525 J = (1/2)(0.0045 kg)v²
Solving for v, we can rearrange the equation as follows:
v² = (2 * PE_initial) / m
v = √((2 * 0.45525 J) / 0.0045 kg)
v ≈ 14.14 m/s
Therefore, the speed of the body just before it strikes the ground, neglecting air resistance, will be approximately 14.14 m/s.