An asteroid is heading towards Mars at the rate of 7.7x10 to the power of 4 mi./hr. If the asteroid is 3.311x10 to the power of 8 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.
To find the number of hours it will take for the asteroid to hit Mars, we can use the formula:
Time = Distance / Rate
Given:
Distance (d) = 3.311x10^8 miles
Rate (r) = 7.7x10^4 mi./hr
Plugging in the values into the formula, we get:
Time = (3.311x10^8 miles) / (7.7x10^4 mi./hr)
To divide the distances and rates, we subtract the exponents of the denominator from the exponent of the numerator:
Time = (3.311/7.7) * (10^8 / 10^4) miles/hr
Simplifying further, we have:
Time = 0.429481 * (10^8-4) miles/hr
Time = 0.429481 * 10^4 miles/hr
Converting scientific notation to decimal notation, we get:
Time = 0.429481 * 10000 miles/hr
Time = 4294.81 miles/hr
Thus, it will take approximately 4294.81 hours for the asteroid to hit Mars.
Expressed in scientific notation, it will be:
Time = 4.29481x10^3 hours.