A$\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{}\mathit{k}\mathit{g}$ teddy bear is nudged off a window sill and falls $\mathbf{2}\mathbf{m}$ to the ground. (a) What is the kinetic energy at the instant it hits the ground? What is its speed? What assumptions or approximations did you make in this calculation?

(b) A $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{kg}$ flowerpot is nudged off a window sill and falls $\mathbf{2}\mathbf{}\mathbf{m}$ to the ground. What is the kinetic energy at the instant it hits the ground? What is its speed? How do the speed and kinetic energy compare to that of the teddy bear in part (a)?

- The mass of a teddy bear is $0.5\mathrm{kg}$

- The height from which the teddy bear falls is $2\mathrm{m}$

- The mass of a flowerpot is $1.0\mathrm{kg}$

- The height from which the flowerpot falls is $2\mathrm{m}$

The kinetic energy is determined when an object is in motion. When the total force is applied on an object, the work done speeds up the object and gets kinetic energy.

The speed is calculated by the following formula,

$v^2=2gH$

where,

$g=$acceleration due to gravity $=9.81\mathrm{m}/{\mathrm{s}}^2$

$H=$height from which the teddy bear falls

Substitute the values in the above expression,

$v=\sqrt{2gH}$

$=\sqrt{2\times 9.81\times 2}$

$=6.26\mathrm{m}/\mathrm{s}$

Hence, the speed of a teddy bear is $6.26\mathrm{m}/\mathrm{s}$

The kinetic energy is calculated by the following formula,

$E=\frac{1}{2}m{v}^2$

where,

$m=$mass of a teddy bear

$v-$speed of a teddy bear

Substitute the values in the above expression,

$E=\frac{1}{2}\times 0.5\times 6.{26}^2$

Hence, the kinetic energy at the instant the bear hits the ground is $9.80\mathrm{J}$

The approximation and assumption made in this calculation is the "g" value which is due to the acceleration of gravity.

The speed is calculated by the following formula,

$v^2=2gH$

where,

$g=$acceleration due to gravity $=9.81\mathrm{m}/{\mathrm{s}}^2$

$H=$height from which the teddy bear falls

Substitute the values in the above expression,

$v=\sqrt{2gH}$

$=\sqrt{2\times 9.81\times 2}$

$=6.26\mathrm{m}/\mathrm{s}$

Hence, the speed of a teddy bear is $6.26\mathrm{m}/\mathrm{s}$

The kinetic energy is calculated by the following formula,

$E=\frac{1}{2}m{v}^2$

Where,

$m=$mass of a teddy bear

$v-$speed of a teddy bear

$E=\frac{1}{2}\times 1\times (6.26{)}^2$

Hence, the kinetic energy at the instant the bear hits the ground is $19.59\mathrm{J}$

The speed of a flowerpot and the bear is the same because both of them fall from the same height $\mathrm{H}$.

The kinetic energy of a flower pot is twice of that of a teddy bear. Because the mass of the flowerpot is twice as the mass of a teddy bear.