In order for a spacecraft to reach Earth's orbital velocity, it must achieve a speed of 17,500 mph in 610 seconds after its first stage burnout where it should have achieved a speed of 1530 mph. What percent increase in speed per second is necessary after first stage in order to accomplish an orbit?

The speed must increase by a factor of 17500/1530 = 11.438

So, we need to find x such that

x^610 = 10.438
x = 1.004

So, the speed must increase by 0.4% each second.

Thank you.That one had me stumped, but the way you explained it makes sense. 0.4%

To determine the percent increase in speed per second after the first stage burnout, we need to calculate the change in speed and divide it by the time taken.

First, let's find the change in speed. The spacecraft needs to achieve a speed of 17,500 mph, and after the first stage burnout, it has already reached a speed of 1530 mph. Therefore, the change in speed is:

17,500 mph - 1530 mph = 15,970 mph

Next, we divide this change in speed by the time taken. In this case, the time taken is 610 seconds. So, the increase in speed per second is:

15,970 mph / 610 seconds = 26.18 mph/second

Finally, to determine the percent increase in speed per second, we need to find what percentage of the initial speed (1530 mph) the increase in speed per second represents.

((26.18 mph/second) / 1530 mph) x 100 = 1.71%

Therefore, a percent increase in speed per second of approximately 1.71% is necessary after the first stage burnout in order to achieve an orbit.