Question

You are flying your Scooty Puff Jr. spaceship at 400 m/s in a direction 40 degrees from the positive y-axis towards the negative x-axis. You're also accelerating at a rate of 0.5 m/s2 in a direction 30 degrees from the positive x-axis towards the negative y-axis. What is your current velocity?

Answer 1

Step-by-step explanation:

Given

velocity of spaceship =400 m/s

at angle of
`40^(\circ)` from Positive Y axis towards negative x axis

acceleration of Spaceship=
`0.5 m/s^2`

at an angle of
`30^(\circ)` from positive x axis towards the negative x axis

`\vec{v}=400\left ( -\sin(40)\hat{i}+\cos (40)\hat{j}\right )`

`\vec{v}=-257.11\hat{i}+306.41\hat{j}`

acceleration

`\vec{a}=0.5\left ( \cos (30)\hat{i}-\sin (30)\hat{j}\right )`

`\vec{a}=0.433\hat{i}-0.25\hat{j}`