An asteroid is heading towards Mercury at a rate of 15.4 times 10 to the 4th power mph. If the asteroid is 6.622 times 10 to the 8th power miles away from mercury ,how many hours will it be before it hits Mercury? Write the answer in scientific notation ,expressed to the exact decimal place.
To calculate the time it takes for the asteroid to hit Mercury, we can use the formula:
Time = Distance / Speed
The distance from the asteroid to Mercury is 6.622 times 10^8 miles, and the speed of the asteroid is 15.4 times 10^4 mph.
Time = (6.622 times 10^8 miles) / (15.4 times 10^4 mph)
To divide these two values, we can divide the numbers and subtract the exponents:
Time = (6.622 / 15.4) times (10^8 / 10^4) miles / mph
Time = 0.429 times 10^4 miles / mph
Now, let's convert miles per hour to hours per mile by taking the reciprocal:
Time = 0.429 times 10^4 hours x mph / mile
Since the units should be hours, we need to multiply by a conversion factor of 1 mile / mph:
Time = 0.429 times 10^4 hours x (mile / mph) x (1 mph / mile)
Time = 0.429 times 10^4 hours
Expressing this in scientific notation, the answer is:
Time = 4.29 times 10^3 hours
To calculate the time it takes for the asteroid to reach Mercury, we need to divide the distance by the speed. Let's break down the steps:
1. Convert the speed from mph to miles per hour in scientific notation:
The speed is given as 15.4 × 10^4 mph.
2. Convert the distance from miles to scientific notation:
The distance is given as 6.622 × 10^8 miles.
3. Calculate the time using the formula: Time = Distance / Speed.
Let's do the calculations:
Step 1: Speed in scientific notation:
15.4 × 10^4 mph
Step 2: Distance in scientific notation:
6.622 × 10^8 miles
Step 3: Time calculation:
Time = Distance / Speed
Time = (6.622 × 10^8 miles) / (15.4 × 10^4 mph)
To divide the numbers in scientific notation, divide the coefficients and subtract the exponents:
Time = (6.622 / 15.4) × 10^(8 - 4) miles/mph
Simplify the coefficient:
Time = 0.42961 × 10^4 miles/mph
The time is expressed as 0.42961 × 10^4 miles/mph. Now, we need to convert it to hours:
There are 60 minutes in an hour and 60 seconds in a minute. Therefore, to convert from miles/mph to hours, we divide by 60^2:
Time = (0.42961 × 10^4 miles/mph) / (60 × 60) seconds/hour
Simplify the exponent:
Time = 0.42961 × 10^(4 - 2) miles/mph
Simplify the coefficient:
Time = 4.2961 × 10^2 miles/mph
Thus, it will take approximately 4.2961 × 10^2 hours (expressed to the exact decimal place) for the asteroid to hit Mercury.
To find the number of hours it will take for the asteroid to hit Mercury, we can use the formula: time = distance / speed.
Given:
Speed (s) = 15.4 × 10^4 mph
Distance (d) = 6.622 × 10^8 miles
We divide the distance by the speed to find the time:
time = distance / speed
time = (6.622 × 10^8 miles) / (15.4 × 10^4 mph)
To divide, we subtract the exponents of the powers of 10 and divide the numbers:
time = (6.622 / 15.4) × (10^8 / 10^4) miles / mph
time = 0.429 × 10^(8-4) miles / mph
time = 0.429 × 10^4 miles / mph
To express the answer in scientific notation, we rewrite it as:
time = 4.29 × 10^3 hours
Therefore, it will take approximately 4.29 × 10^3 hours for the asteroid to hit Mercury.