A drone follows the flight pattern and for

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

A drone follows the flight pattern

x(t)=\tfrac{5t}{1+t^{2}}

and

y(t)=\tfrac{3}{1+t^{2}}

for

t>0

, where

t

is measured in seconds and distances are in meters. (1) Compute the slope of the drone's trajectory at

t=2

and simplify your answer completely. (2) Determine the acute angle

\alpha

(in radians) that the trajectory makes with the positive

x

-axis at

t=2

. Express

\alpha

exactly, not as a decimal approximation. (3) Discuss whether the drone's path is becoming steeper or flatter as

t

increases beyond

2

. Support your conclusion using appropriate calculus reasoning without resorting to numerical graphing tools.