Question

The trajectory of a flying saucer is given by the vector function r(t) = (5 sin(t))i + (5 cos(t))j + 12tk for t ≥ 0 where coordinate is measured in miles and time in minutes. Find the time moment t0 when the flying saucer travels exactly the distance 26 miles along the curve from the starting point.

Answer 1

Answer:

t0 = 2

Step-by-step explanation:

r' = <5cost,-5sint,12>

ds = $\sqrt{25cos^{2}t+25sin^{2}t+12^2} = \sqrt{25+144} = 13$ dt

So, we want

$\int\limits^x_0 {13} \, dt = 26$