# We need to find the energy equivalent and the speed. Can I get some help please? Thanks!

Oct 26, 2017

A) $E = 4.5 \cdot {10}^{17} J$
B) $v = 120 \frac{m}{s}$#

#### Explanation:

A) This calls for Einstein's famous formula
$E = m \cdot {c}^{2}$

Plugging in the data,

$E = 5 k g \cdot {\left(3 \cdot {10}^{8} \frac{m}{s}\right)}^{2} = 5 k g \cdot 9 \cdot {10}^{16} {m}^{2} / {s}^{2}$

So $E = 45 \cdot {10}^{16} k g \cdot {m}^{2} / {s}^{2} = 4.5 \cdot {10}^{17} k g \cdot {m}^{2} / {s}^{2}$

We want units that indicate energy, so group the units we have so that you can see force*distance (which is how you calculate work).

$E = 4.5 \cdot {10}^{17} \left(k g \cdot \frac{m}{s} ^ 2\right) \cdot m = 4.5 \cdot {10}^{17} J$

B) Use the suvat formula
$v = u + a \cdot t$

Without air resistance, the acceleration = $g = 9.8 \frac{m}{s} ^ 2$.
$v = 0 + 9.8 \frac{m}{s} ^ 2 \cdot 12 s = 117.6 \frac{m}{s}$,
$\text{or, with 2 significant digits} , 120 \frac{m}{s} .$

I hope this helps,
Steve