Answer:
A. Vx = 3.63 m/s
B. Vy = -45.73 m/s
C. |V| = 45.87 m/s
D. θ = -85.46°
Explanation:
Given that position, r, is given as:
r = 3.63tˆi − 5.73t^2ˆj + 8.16ˆk
Velocity is the derivative of position, r:
V = dr/dt = 3.63 - 11.46t^j
A. x component of velocity, Vx = 3.63 m/s
B. y component of velocity, Vy = -11.46t
t = 3.99 secs,
Vy = - 11.46 * 3.99 = -45.73 m/s
C. Magnitude of velocity, |V| = √[(-45.73)² + 3.63²]
|V| = √(2091.2329 + 13.1769)
|V| = √(2104.4098)
|V| = 45.87 m/s
D. Angle of the velocity relative to the x axis, θ is given as:
tanθ = Vy/Vx
tanθ = -45.73/3.63
tanθ = -12.6
θ = -85.46°
The electric field is given by volts/distance:

. The breakdown voltage of dry air is about 3x10^6V/m. So solving for V we get

or
<h3><em><u>given</u></em><em><u>:</u></em></h3>
<em><u>first</u></em><em><u> </u></em><em><u>trip</u></em><em><u>=</u></em><em><u> </u></em><em><u>5</u></em><em><u>0</u></em><em><u> </u></em><em><u>miles</u></em><em><u>.</u></em>
<em><u>second</u></em><em><u> </u></em><em><u>trip</u></em><em><u>=</u></em><em><u> </u></em><em><u>3</u></em><em><u>0</u></em><em><u>0</u></em><em><u> </u></em><em><u>miles</u></em><em><u>.</u></em>
<h3><em><u>to</u></em><em><u> </u></em><em><u>find</u></em><em><u>:</u></em></h3>
<em><u>his</u></em><em><u> </u></em><em><u>new</u></em><em><u> </u></em><em><u>time</u></em><em><u> </u></em><em><u>compared</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>old</u></em><em><u> </u></em><em><u>time</u></em><em><u>.</u></em>
<h3><em><u>solution</u></em><em><u>:</u></em></h3>
<em><u>Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.</u></em>
<em><u>Speed = Distance/Time</u></em>
<em><u>So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.</u></em>
<em><u>= 100/x hr</u></em>
<em><u>Therefore</u></em><em><u>,</u></em><em><u> </u></em><em><u>his new time compared with the old time was twice as much.</u></em>
<em><u>answer</u></em><em><u>=</u></em><em><u> </u></em><em><u>b</u></em><em><u>)</u></em><em><u> </u></em><em><u>twice</u></em><em><u> </u></em><em><u>as</u></em><em><u> </u></em><em><u>much</u></em>