Rocket Answer Number 2
Between you and me, it makes me giggle to read this aloud. Thanks to Jodie's Engineer friend Rachel for this answer.
First you would have to know the height of Big Jet when he dropped the soup, and the distance at that specific moment between Big Jet and Rocket and the elevation of Rocket. You would also need to know the maximum acceleration rate for each gear as Rocket ramps up his speed. And the maximum speed at which the ship can attain. After that, you are essentially solving an equation for a triangle. (vector analysis of Rocket's ship in the x, y and z direction and just the y of the bowl of soup assuming it is a straight fall.)
Set the two equations equal to each other--which is math for where the bowl and Rocket meet--then solve for time.
Otherwise, assuming Big Jet and Rocket are side by side and both the bowl of soup and rocket have initial speed of zero and linear acceleration ramping up to speed...
the distance the bowl travelled = 0.5*a * t^2 = 0.5*32 ft/s/s * 90 seconds^2 = 129,600 ft = 24 mi
Assuming the average speed of rocket is a linear average and Rocket's initial z speed is zero...
the average speed of rocket = 24 mi /90 seconds = 960 miles per hour
Meaning that if he started at zero miles per hour, he would be at 1920 miles per hour by the time he reaches the bowl.
Now negating air friction is a serious error in this calculation. Ask a physicist dot com says that a human free fall reaches terminal velocity within 400 yards. So depending on how much the bowl of soup weighs, and the cross sectional area of the bowl perpendicular to the earth, it is probably reasonable to assume that the bowl reached terminal velocity within seconds of its descent. And if the bowl was falling at a a constant speed instead of continually accelerating 32 ft/sec, then Rocket would have much less distance to clear before catching up with the bowl.
And if Rocket was travelling laterally at all (as it seems to be in the description below), then the cosine of the angle time his speed would be fully dedicated to making up the x distance between him and the bowl. So the absolute speed of Rocket would end up being the square root of his vertical speed squared (in the case above 960 miles per hour) plus his lateral speed squared.
First you would have to know the height of Big Jet when he dropped the soup, and the distance at that specific moment between Big Jet and Rocket and the elevation of Rocket. You would also need to know the maximum acceleration rate for each gear as Rocket ramps up his speed. And the maximum speed at which the ship can attain. After that, you are essentially solving an equation for a triangle. (vector analysis of Rocket's ship in the x, y and z direction and just the y of the bowl of soup assuming it is a straight fall.)
Set the two equations equal to each other--which is math for where the bowl and Rocket meet--then solve for time.
Otherwise, assuming Big Jet and Rocket are side by side and both the bowl of soup and rocket have initial speed of zero and linear acceleration ramping up to speed...
the distance the bowl travelled = 0.5*a * t^2 = 0.5*32 ft/s/s * 90 seconds^2 = 129,600 ft = 24 mi
Assuming the average speed of rocket is a linear average and Rocket's initial z speed is zero...
the average speed of rocket = 24 mi /90 seconds = 960 miles per hour
Meaning that if he started at zero miles per hour, he would be at 1920 miles per hour by the time he reaches the bowl.
Now negating air friction is a serious error in this calculation. Ask a physicist dot com says that a human free fall reaches terminal velocity within 400 yards. So depending on how much the bowl of soup weighs, and the cross sectional area of the bowl perpendicular to the earth, it is probably reasonable to assume that the bowl reached terminal velocity within seconds of its descent. And if the bowl was falling at a a constant speed instead of continually accelerating 32 ft/sec, then Rocket would have much less distance to clear before catching up with the bowl.
And if Rocket was travelling laterally at all (as it seems to be in the description below), then the cosine of the angle time his speed would be fully dedicated to making up the x distance between him and the bowl. So the absolute speed of Rocket would end up being the square root of his vertical speed squared (in the case above 960 miles per hour) plus his lateral speed squared.
posted by brian at
8:50 AM
0 Comments:
Post a Comment
<< Home