To find out how many hours it will take for the asteroid to hit Mars, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Given:
- Distance = \(3.311 \times 10^8\) miles
- Speed = \(7.7 \times 10^4\) miles/hr
Now, we can substitute the values into the formula:
\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ miles/hr}} \]
To divide these numbers in scientific notation, we divide the coefficients and subtract the exponents:
\[ \text{Time} = \frac{3.311}{7.7} \times 10^{8 - 4} = \frac{3.311}{7.7} \times 10^4 \]
Calculating \(\frac{3.311}{7.7}\):
\[ \frac{3.311}{7.7} \approx 0.430 \]
Now, substituting this back into our equation, we have:
\[ \text{Time} \approx 0.430 \times 10^4 \]
Now, we can convert \(0.430\) into scientific notation:
\[ 0.430 = 4.30 \times 10^{-1} \]
Thus:
\[ \text{Time} \approx 4.30 \times 10^{-1} \times 10^4 = 4.30 \times 10^{3} \]
Therefore, the time it will take for the asteroid to hit Mars is:
\[ \text{Time} \approx 4.30 \times 10^3 \text{ hours} \]