Question

A pure silver lions fan throws a roll of toilet paper at 7.2 m/s from her seat at Ford‘s field during a recent game. how fast is the 0.4 KG roll going when it strikes an opposition player 16. 1 m below?

Answer 1

Given:

The mass of the roll is m =0.4 kg.

The velocity of the roll is v = 7.2 m/s at a height h = 16.1 m.

To find the velocity when it strikes the opposition player, where height h'= 0 m

Explanation:

According to the law of conservation of energy, the total energy is always conserved, so

$\begin{gathered} (P\mathrm{}E\mathrm{})_h+(K\mathrm{}E.)_h=(P.E.)_{h^{\prime}}+(K.E.)_{h^{\prime}} \\ mgh+\frac{1}{2}mv^2=mgh^{\prime}+\frac{1}{2}mv^{\prime2} \end{gathered}$

Here, g = 9.8 m/s^2 is the acceleration due to gravity.

On substituting the values, the velocity will be

$\begin{gathered} 0.4\times9.8\times16.1+\frac{1}{2}\times0.4\times(7.2)^2=0.4\times9.8\times0+\frac{1}{2}\times0.4v^{\prime2} \\ 63.112+10.368=0+0.2v^{\prime2} \\ v^{\prime}=19.17\text{ m/s} \end{gathered}$

Final Answer: The velocity of the roll when it strikes the player is 19.17 m/s