An asteroid is heading toward Mars at the rate of 7.7 x 10^4 mi./hr. If the asteroid is 3.311 x 10^8 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.
the answer is 4.3x 10^3
To find the time it will take for the asteroid to hit Mars, we need to divide the distance to Mars by the rate of the asteroid.
Distance to Mars: 3.311 x 10^8 miles
Rate of the asteroid: 7.7 x 10^4 mi./hr
Time = Distance / Rate
Time = (3.311 x 10^8 miles) / (7.7 x 10^4 mi./hr)
To divide two numbers written in scientific notation, we divide their coefficients (numbers before the multiplication sign) and subtract their exponents (numbers after the multiplication sign).
Time = (3.311 / 7.7) x 10^(8 - 4) miles/hr
Time = 0.42935 x 10^4 miles/hr
Since the time is in hours, we can simplify the units as follows:
Time = 4.2935 x 10^3 hr
Therefore, it will be approximately 4.2935 x 10^3 hours before the asteroid hits Mars.
To find the number of hours it will take for the asteroid to hit Mars, we can use the formula:
time = distance / rate
Given that the asteroid is 3.311 x 10^8 miles away from Mars and is moving at a rate of 7.7 x 10^4 mi./hr, we can substitute the values into the formula to calculate the time:
time = (3.311 x 10^8 miles) / (7.7 x 10^4 mi./hr)
To divide these values, we will subtract the exponents (10^8 - 10^4) and divide the coefficients (3.311 / 7.7):
time = 4.29481 x 10^(8 - 4) hours
time = 4.29481 x 10^4 hours
Therefore, the asteroid will take approximately 4.29481 x 10^4 hours to hit Mars.
To calculate the time it will take for the asteroid to hit Mars, we can use the formula:
Time = Distance / Speed
Given:
Distance = 3.311 x 10^8 miles
Speed = 7.7 x 10^4 mi./hr
Substituting the values into the formula, we get:
Time = (3.311 x 10^8 miles) / (7.7 x 10^4 mi./hr)
To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents:
Time = (3.311 / 7.7) x 10^(8 - 4) miles / mi.
Simplifying the division, we get:
Time = 0.429221 x 10^4 miles / mi.
Since the units cancel out, we are left with:
Time = 0.429221 x 10^4 hr.
Therefore, it will take approximately 0.429221 x 10^4 hours, or 4292.21 hours, for the asteroid to hit Mars.