A rocket has been launched from Russia International Terminal towards the point (√tk, 〖te〗^k, k) at a speed 2000 feet/second. What is the position of the rocket after half an hour?
just integrate each component. 0 to 1800 seconds.
(1.944×10^9)k , 1.62×10^6 e^k , 0
To find the position of the rocket after half an hour, we need to determine the values of t and k.
Given that half an hour is equivalent to 30 minutes, we can use this value for t.
Let's substitute t = 30 minutes into the equation (√tk, 〖te〗^k, k) to find the position of the rocket:
x-coordinate: (√(30 * k))
y-coordinate: (e^(30 * k))
z-coordinate: k
As for the value of k, it is not provided in the question. It could be any real number. So, without more information, we cannot determine the exact position of the rocket after half an hour. However, we can calculate the position for a specific value of k.
For example, if we assume k = 1, we can calculate the position of the rocket after half an hour as follows:
x-coordinate: (√(30 * 1)) = √30
y-coordinate: (e^(30 * 1)) = e^30 (approximately 1.07 x 10^13)
z-coordinate: 1
Therefore, the position of the rocket after half an hour, assuming k = 1, would be (√30, approximately 1.07 x 10^13, 1).