The length of a rocket is 100 m on the earth. When it was flying an observer on the earth measured its length as a 99m. Calculate the speed of the rocket. i. 3.78×107ms−13.78×107��−1 ii. 6.3×107ms−16.3×107��−1 iii. 7.8×107ms−17.8×107��−1 iv. 4.24×107ms−
Question
The length of a rocket is 100 m on the earth. When it was flying an observer on the earth measured its length as a 99m. Calculate the speed of the rocket.
i.
3.78×107ms−13.78×107��−1
ii.
6.3×107ms−16.3×107��−1
iii.
7.8×107ms−17.8×107��−1
iv.
4.24×107ms−
Solution
The question is asking for the speed of the rocket based on the length contraction observed. This is a concept from Einstein's theory of special relativity. The formula for length contraction is:
L = L0 * sqrt(1 - v^2/c^2)
where: L is the contracted length (99m in this case), L0 is the proper length (100m in this case), v is the speed of the rocket, which we are trying to find, c is the speed of light (approximately 3*10^8 m/s).
We can rearrange the formula to solve for v:
v = sqrt(c^2 * (1 - (L/L0)^2))
Substituting the given values:
v = sqrt((3*10^8 m/s)^2 * (1 - (99m/100m)^2))
v = sqrt((9*10^16 m^2/s^2) * (1 - 0.9801))
v = sqrt((9*10^16 m^2/s^2) * 0.0199)
v = sqrt(1.791*10^15 m^2/s^2)
v = 4.23*10^7 m/s
So, the speed of the rocket is approximately 4.23*10^7 m/s. The closest answer to this is option iv. 4.24×10^7 m/s.
Similar Questions
A 5 kg model rocket is lifted off the ground by a force of 80 N. At a height of 10 m, what is the speed of the rocket? Use g = 10 m/s2Question 1Answera.17.89 m/sb.14.76 m/sc.21.99 m/sd.10.95 m/se.35.9 m/s
A rocket is travelling at a speed of 21,000 miles per hour (mph). Use the fact that 1 km is approximately equal to 0.6214 miles to convert this speed to kilometers per hour (km/h). Round your answer to the nearest whole number. Do not type the units in the space below.
Ten seconds after liftoff, a rocket reaches a speed of 60 m/s. Calculate its average acceleration during this time.
You measure the length of a passing Clingon spacecraft to be 155 m. If the Clingon spacecraft is moving at 0.58 the speed of light, what would be its length in metres if it was at rest relative to you? Give your answer to the nearest whole number.
What is the velocity of a rocket that goes 700 km north in 25 seconds?A3 kilometers per second northB725 miles per hourC30 kilometers per second southD4 meters per second
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.