Question

An asteroid is heading toward Mars at the rate of 7.7 × 10* mi./hr. If the asteroid is 3.311 × 108 miles away from Mars, how many hours will it be before it hits Mars?
Write the answer in scientific notation, expressed to the exact decimal place.

Answer 1

To determine 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 to Mars = \(3.311 \times 10^8\) miles
- Speed of the asteroid = \(7.7 \times 10^6\) miles/hour

Now, we can plug these values into the formula:

\[
\text{Time} = \frac{3.311 \times 10^8}{7.7 \times 10^6}
\]

To simplify this, we'll divide the coefficients and subtract the exponents (since they are in scientific notation):

1. Divide the coefficients:

\[
\frac{3.311}{7.7} \approx 0.430
\]

2. Subtract the exponents:

\[
10^8 / 10^6 = 10^{8-6} = 10^2
\]

3. Combine the results:

\[
\text{Time} \approx 0.430 \times 10^2
\]

4. Convert to proper scientific notation:

\[
0.430 \times 10^2 = 4.30 \times 10^1
\]

Thus, the time it will take for the asteroid to hit Mars is:

\[
\boxed{4.30 \times 10^1} \text{ hours}
\]