The planet Neptune has a radius of 15000 miles and rotates one revolution every 18 hours. What is the linear speed of a point on its equator, in miles per hours?
since C = 2πr, and speed = distance/time,
speed = 2π*15000 mi/18 hr = 5236 mi/hr
Well, if Neptune rotates pretty quickly, it's not going to be the most reliable planet for keeping time, is it? It must have a lot on its schedule! Anyway, let's get to the math.
The linear speed of a point on the equator can be calculated by finding the circumference of the planet and dividing it by the time it takes for one full rotation.
The circumference of a circle can be found using the formula C = 2πr, where r is the radius. So, the circumference of Neptune would be 2π * 15000 miles.
Now, let's convert the 18 hours to minutes. There are 60 minutes in an hour, so 18 hours would be 18 * 60 = 1080 minutes.
To find the speed in miles per hour, we need to divide the circumference by the time it takes for one full rotation. In this case, 2π * 15000 miles divided by 1080 minutes.
Now, if we simplify it a bit, we get (2 * 3.14 * 15000) miles / 1080 minutes.
And if we do the math, the linear speed of a point on Neptune's equator would be approximately... 328.7 miles per hour! So hold on tight if you're ever planning a visit to Neptune, because it's spinning faster than a clown on a unicycle!
To calculate the linear speed of a point on Neptune's equator, we need to determine the circumference of the planet's equator and divide it by the time taken for one revolution.
1. Firstly, we calculate the circumference of Neptune's equator using the formula: Circumference = 2 * π * radius
= 2 * π * 15000 miles
= 30000π miles
2. Next, we need to convert the time taken for one revolution to hours. Since there are 24 hours in a day, we divide the time by 24:
18 hours / 24 = 0.75 days
3. Now, we calculate the linear speed of a point on Neptune's equator by dividing the circumference by the time taken for one revolution:
Linear speed = Circumference / Time taken
= (30000π miles) / (0.75 days)
= 40000π miles per day
4. Finally, to convert the linear speed from miles per day to miles per hour, we divide by 24:
Linear speed = 40000π miles per day / 24
= 1666.67π miles per hour
Therefore, the linear speed of a point on Neptune's equator is approximately 1666.67π miles per hour.
To find the linear speed of a point on the equator of Neptune, we need to know the circumference of the planet's equator. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
In this case, the radius of Neptune is given as 15000 miles. Plugging this value into the formula, we get:
C = 2π * 15000 = 30000π miles
Now, we know that Neptune rotates one revolution every 18 hours. To find the linear speed, we need to convert this to miles per hour.
Since there are 24 hours in a day, the conversion factor is:
1 day = 24 hours
Therefore, the linear speed can be calculated as:
Linear Speed = (Circumference of Equator) / Time to Complete One Revolution
Linear Speed = (30000π miles) / (18 hours) * (1 day / 24 hours)
Now, let's simplify and calculate the linear speed:
Linear Speed = 30000π / 18 * 1/24 miles per hour
= 500π / 9
Using an approximation of π ≈ 3.14, we can evaluate the expression:
Linear Speed ≈ 500 * 3.14 / 9
≈ 174.89 miles per hour
Therefore, the linear speed of a point on Neptune's equator is approximately 174.89 miles per hour.