Two spacecraft are 13,500 m apart and moving directly toward each other. The first spacecraft has velocity 525?
Two spacecraft are 13,500 m apart and moving directly toward each other. The first spacecraft has velocity 525 m/s and accelerates at a constant −15.5 m/s2. They want to dock, which means they have to arrive at the same position at the same time with zero velocity. (a) What should the initial velocity of the second spacecraft be? (b) What should be its constant acceleration?
Two spacecraft are 13,500 m apart and moving directly toward each other. The first spacecraft has velocity 525?
Two spacecraft are 13,500 m apart and moving directly toward each other. The first spacecraft has velocity 525 m/s and accelerates at a constant −15.5 m/s2. They want to dock, which means they have to arrive at the same position at the same time with zero velocity. (a) What should the initial velocity of the second spacecraft be? (b) What should be its constant acceleration?
How long would it take a spacecraft to travel one light-year?
Very good question. Here’s my answer:I asked the exact same question to myself a long time ago.Let’s assume that you’re riding on a spacecraft at the same speed of the New Horizons probe, which goes at an incredible speed of 36,373 mph, or Mach 47. To see how long it would take us to travel a light year, we must first have to know what a light-year is. A light-year has an exagerated distance of about 6 trillion miles.This is going to sound unrealistic, however, it’s the truth. It would take you little under 20,000 years, to travel just 1 light-year. Let’s say that you want to travel to Kepler 438b, which is over 400 light-years away. If you wanted to travel there in the fastest spacecraft made by man (New Horizons), it would take you about 2 million years. New Horizons probe:When I found out, I was baffled to see how far those other planets where. It seems that we are stuck here, because we do not have the technology to reach any other habitable planets in under a human’s lifetime. I wish we would be able to travel at such speeds, however, we are just too far from achieving such technologies.It’s nice to see people are interested in this subject. Hope I helped.
Is re-entering the atmosphere slowly an option for a spacecraft, and could a slow re-entry be safer for humans?
Yes, and no. Do you know how much fuel it takes to get out of the atmosphere? Well, it would take about the same amount to slowly drop into the atmosphere.Assuming you are in orbit, you would have to slow enough to be able to drop at a lateral speed of less than 1000MPH. Which would take a LOT of fuel.Then you would have to (mostly) support the weight of the ENTIRE spacecraft as it slowly descended (let’s say < 500MPH for most of it), and then get to zero MPH as you landed. So you would have to burn enough fuel to counteract gravity for at least 30 minutes, but taking into account having to slow down as well, easily over an hour. If you combine the slow-down and descent into a nice ballistic curve, it might be possible. But the cones by which the exhaust of the rocket power your slowdown aren’t very aerodynamic, and so would have to be rather stronger than what is needed for ascent to withstand the buffeting they would endure. Unless you slowed down a LOT before ever getting into the atmosphere.And do you take all this extra fuel up with you, and create some way to refuel once you were in orbit?? Taking all that re-entry fuel with you is going to expand the amount needed to get to orbit, and it keeps going back and forth and increasing. Even if you could refuel in orbit, you would have to modify your entire spacecraft to be able to hold the fuel needed for descent. I doubt it would need to be made anymore strong, as most re-entry vehicles are pretty sturdy.But it would just take too much fuel to be in any way economical, when all you need to have is enough to slow down enough to get into the atmosphere and then use aero-braking and parachutes to be able to land pretty softly.
How to convert km/h to m/s? What is the distance traveled by a car in 1 second at 72 km/h?
Everytime that you need to convert a value given in kmph (kilometer per hour) to m/s (meters per second), there is a very easy way to do this.To convert a value in kmph to m/s, multiply it by 5/18.To convert a value given in m/s to kmph, multiply it by 18/5.So, if the car is going at 72kmph, then its speed in m/s will be 72 x 5/18 = 20 m/s.Thus, the car travels 20 meters in one second.Similarly, if the car is travelling at 90kmph, then converting it to m/s : 90 x 5/18 = 25m/s.Hope my answer helps.Cheers!Ps: Thank you Shruti Kumari for A2A
If the earth is rotating at a high speed and we jump up, why doesn't the earth move below us at high speed?
Since other answers have correctly mentioned the atmosphere and such, let's take it out of the equation for the sake of argument and see what happens.In terms of the difference in the helicopter's path vs. the ground, let's look at what happens during one whole day as the Earth rotates. Assuming the helicopter can perform an ideal, vertical-acceleration-only hover, then the surface of the Earth and the helicopter have the same tangential speed as the Earth turns, due to conservation of momentum. But, since the helicopter is now a few feet (~1 meter) above the ground, the path the helicopter takes to go around the Earth during one day is now slightly longer as compared to the surface itself. The added circumference of that trip all the way around the Earth for the helicopter turns out be just 2 times Pi times the height above the ground. It takes the Earth just under 24 hours to rotate once on its axis, so the helicopter would have to move at an additional horizontal speed of maybe 18 feet (~5.5 meters) per 24 hours, or something like 0.00014 miles per hour (~0.00022 km/h) to stay directly over the same spot on the ground. This is such a negligible difference in horizontal speed that you don't notice it in any practical system.A real helicopter would deviate horizontally by a speed that is orders of magnitude more than that when it takes off anyway. And, of course, helicopters fly in the atmosphere, which is coupled to the ground. It's also fair to say that wind speed dominates any effects from conservation of momentum, as it's orders of magnitude larger, even at high altitudes. So, real aircraft worry about the difference in wind speed and direction vs. the ground, rather than orbital mechanics.
If I was going the speed of light and travelled 10 light years, would that be 10 years to someone on earth or 10 years to me?
It depends on your frame of reference. The change in time is described by rthe Lorentz transformation, which is: If you were standing on Earth, and you said "I want to travel 10 light years," you could effectively reach any place 10 lightyears from Earth. That means, from Earth, if we watched your spacecraft hurtle towards your remote destination of choice, we would see it taking 10 years. This is t in the above equations.But, if you brought a timer/calendar on board the spacecraft with you, you would measure the altered time, which is t' in the above equations. My background on this is a bit rusty, so I hope other Quorites keep me honest, but the faster you move, the larger the subtraction term becomes in the Lorentz equation. This means, since you are moving near or at the speed of light, this term will approach x/c, which is larger than vx/c^2, making the time dilation more pronounced. (fyi, gamma is less than 1 but approaches 1 as v approaches c). So to answer your question, it's 10 years from your original observation point, mainly because that is where you decide to "travel 10 light years" from. If you are on the ship, you would experience less time. You can figure out the time using the equations above, but it's late and my head hurts. I'll let someone else tackle that for you :)
How great would the damage be if a grain of sand were to hit the Earth at 99% of the speed of light?
Sigh.Look, use the internet, find the answer. Took me about 15 seconds.When you do it that way, you can be more certain of your answer, because if nothing else you’re not buying into anyone else’s mistakes or misinformation—and you’ve been fed at least a little of that. I was going to comment on another answer, but by the time I was done, it was an answer in and of itself.So. (Cracks knuckles, puts fingers to keyboard):The KE equation isKE =(1/2)mv^2For relativistic speeds, we need to adjust the mass by the fraction of c it’s travelling, that’s where things get exciting, but not that much. You’d think 0.9999 could be approximated to “1,” but turns out decimal values are really important here.Annnnnyway……redoing the math, the energy release is about 16.5 KT. Or just about 1.1 Hiroshima bombs.But come on. It’s a grain of sand. It won’t make it through the atmosphere—the X- and gamma-rays generated by the impact will sublimate the grain before anything serious can happen. There will be a “pop,” of bright light and people will say WTF, and only scientists will care.Oh and just to be safe, I re-did the math at Wolfram Alpha’s Relativistic Kinetic Energy Calculator.Computational Knowledge EngineYou’re welcome.
An object is dropped from a height of 500 meters. When will the object reach the ground? With what speed will it hit the ground?
Use following equations to get the answerTo calculate the time for it to reach the ground is given by[math]t=\sqrt{\dfrac{2s}{a}}[/math]Where s is 500 meter and a = g = 10 [math]m/s^2[/math]To calculate velocity use equation [math]v^2=2as[/math] or [math]v=at[/math]
How does a satellite orbit without falling into the Earth?
Man-made satellites don't fall out of space for the same reason that the moon (a big satellite) doesn't crash into the earth, or that the Earth doesn't crash into the Sun. The reason is actually described through Newton's laws of motion.A moving object will continue to move in a straight line at the same speed unless a force acts on it. For an object to move in a circle, a force has to act on it all the time.This force is called the centripetal force. It acts towards the centre of the circle. Gravity is the centripetal force that keeps planets moving around the Sun, and satellites moving around planets.Gravity is the universal force of attraction between masses. It provides the centripetal force needed to keep a satellite in orbit around a planet, or a planet in orbit around a star such as the Sun.Even though gravity pulls on the satellites, they are moving. Satellites don't ever slow down in their orbits since there's almost no friction in space. The result is that they just spin around the sun, never actually falling in.If nothing pulled on them they would just keep going and end up going farther away from the earth. However, the earth's gravity pulls back down. The end result is that they move in a circle around the earth - in an orbit.A Satellite as a ProjectileCircular Motion Principles for SatellitesMathematics of Satellite Motion