What is the maximum height of a shelf where a vase can be placed without breaking if it can withstand a fall speed of 5.0 m/sec?

To determine the maximum height from which a vase can fall without exceeding a fall speed of 5.0 m/s, we can use the principles of physics involving free fall and energy conservation.

When an object falls freely under the influence of gravity, its speed increases as it descends. The speed of the object just before it hits the ground can be calculated using the equation for the speed of an object in free fall:

[ v = \sqrt{2gh} ]

where:

• ( v ) is the final speed (5.0 m/s in this case),
• ( g ) is the acceleration due to gravity (approximately 9.81 m/s²),
• ( h ) is the height from which the object falls.

Rearranging this formula to solve for height ( h ):

[ h = \frac{v^2}{2g} ]

Substituting the known values:

[ h = \frac{(5.0 , \text{m/s})^2}{2 \times 9.81 , \text{m/s}^2} ]

[ h = \frac{25}{19.62} ]

[ h \approx 1.28 \