An asteroid is heading toward Mars at the rate of 7.7×104 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.

Question

Create a striking image of a vast, deep space with billions of stars scattered across the darkness. In the center of this spatial expanse, Mars, depicted as a red, dusty planet with visible craters and valleys, glows against the dark background. Approaching Mars from the right is an asteroid, streaked with shades of gray and black, with small pieces breaking off as it hurtling through space. The asteroid is shown in motion, leaving a faint trail behind, emphasizing its speed and imminent collision. Note that there should be no text in the image.

An asteroid is heading toward Mars at the rate of 7.7×104 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 find out how many hours it will take before the asteroid hits Mars, we need to divide the distance between the asteroid and Mars by the rate at which the asteroid is moving towards Mars.

Distance = 3.311×10^8 miles
Rate = 7.7×10^4 mi./hr

Hours = Distance / Rate

Hours = (3.311×10^8 miles) / (7.7×10^4 mi./hr)

Simplifying the expression, we have:

Hours = (3.311/7.7) × (10^8/10^4)

Hours = 0.429 × 10^(8-4)

Hours = 0.429 × 10^4

Therefore, it will take approximately 0.429 × 10^4 hours before the asteroid hits Mars.

Answer 2

To determine the time it will take for the asteroid to hit Mars, we can use the formula:

Time = Distance / Speed

Given the distance of 3.311×10^8 miles and the speed of 7.7×10^4 mi./hr, we can substitute these values into the formula to get:

Time = (3.311×10^8) / (7.7×10^4)

Now, let's simplify this expression. When dividing numbers written in scientific notation, we divide the coefficients and subtract the exponents:

Time = (3.311 / 7.7) × (10^8 / 10^4)

Simplifying further, we get:

Time = 0.429 × 10^(8-4)
Time = 0.429 × 10^4

Since the exponent is positive, we can rewrite the expression in scientific notation:

Time = 4.29 × 10^3

Therefore, it will be approximately 4.29 × 10^3 hours before the asteroid hits Mars.

Answer 3

To calculate the time it takes for the asteroid to hit Mars, we can use the formula:

Time = Distance / Rate

Given:
Rate = 7.7×10^4 mi./hr
Distance = 3.311×10^8 miles

Plugging the values into the formula, we have:
Time = (3.311×10^8) / (7.7×10^4)

To divide the numbers in scientific notation, we subtract the exponents:
Time = 3.311×10^(8-4) / 7.7

Simplifying further:
Time = 3.311×10^4 / 7.7

Now, divide the numbers:
Time ≈ 4296.1

Expressing the answer in scientific notation, we have:
Time = 4.296×10^3 hours

Therefore, it will take approximately 4.296×10^3 hours for the asteroid to hit Mars.