Dynamics Session 2 Example 2 (ENGR5004)

Dynamics Session 2 Example 2TutorialCurrent specThird8 min

ENGR5004 Dynamics Session 2 worked example 2 (slide 16) official answers

A helicopter is instrumented with an $x$ - $y$ - $z$ accelerometer. During a test flight that starts from rest at the origin at $t = 0$ , the acceleration components recorded in the interval $t = 0$ to 10 s are

$a_x = 0.6t\ \text{m/s}^2, \qquad a_y = 1.8 - 0.36t\ \text{m/s}^2, \qquad a_z = 0$

( $x$ horizontal, $y$ vertical).

Formulas you may need

Cartesian components: $v_x = \displaystyle\int a_x\,dt$ , $x = \displaystyle\int v_x\,dt$ (and the same for $y$ , $z$ ) (learn this)

(a)
Find the helicopter's velocity components and position as functions of time.
(b)
Evaluate the position $(x, y)$ and the speed at $t = 10$ s, and sketch the flight path $y$ against $x$ .
x (t = 10 s) =m
y (t = 10 s) =m
speed (t = 10 s) =m/s