A cannonball of mass 7 kg is shot from a cannon straight up into the air, with an initial velocity of 50 m s⁻¹ - Leaving Cert Physics - Question a - 2019

The kinetic energy (KE) of an object can be calculated using the formula: $KE = \frac{1}{2} mv^2$ For the cannonball:

• Mass (m) = 7 kg
• Velocity (v) = 50 m/s

Substituting the values: $KE = \frac{1}{2} \times 7 \times (50)^2 = 8750 \text{ J}$

The kinetic energy is converted into potential energy as the cannonball rises.

To calculate the greatest height (h) reached, we can use the conservation of energy principle, where the initial kinetic energy equals the potential energy at the highest point: $KE = PE$ $8750 = mgh$ Where:

• m = 7 kg
• g = 9.8 m/s²

Rearranging for h: $h = \frac{KE}{mg} = \frac{8750}{7 \times 9.8} \approx 127.55 m$

To calculate the density ( ho) of the cannonball, use the formula: $\rho = \frac{m}{V}$ Where:

• m = 7 kg
• V = 0.0009 m³

Substituting the values: $\rho = \frac{7}{0.0009} \approx 7777.78 \text{ kg/m}^3$