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Substituting \( a = 20 \, \text{m/s}^2 \) and \( t = 10 \, \text{s} \),
\( d = \frac{1}{2} \times 20 \times (10)^2 = \frac{1}{2} \times 20 \times 100 = 1,000 \, \text{m} \).
The orbital radius of a satellite around Earth is 7,000 km. Using the formula \( v = \sqrt{\frac{GM}{r}} \) (where \( GM = 3.986 \times 10^{14} \, \text{m}^3/\text{s}^2 \)), find the orbital speed in m/s.
Convert radius to meters: \( r = 7,000,000 \, \text{m} \)
\( v = \sqrt{ \frac{3.986 \times 10^{14}}{7,000,000} } = \sqrt{5.694 \times 10^7} \approx 7,546 \, \text{m/s} \)
#### 7,546
A spacecraft performs a burn to increase its velocity by 350 m/s. If its initial speed was 7,200 m/s, what is its new kinetic energy per kg? Use \( KE = \frac{1}{2} v^2 \).
New speed = 7,200 + 350 = 7,550 m/s
\( KE = \frac{1}{2} \times (7,550)^2 = \frac{1}{2} \times 57,002,500 = 28,501,250 \, \text{J/kg} \)
#### 28,501,250
