solve the following vector problems a) A plane leaves the airport on a bearing 4
ID: 3308511 • Letter: S
Question
solve the following vector problems
a) A plane leaves the airport on a bearing 45° travelling a 400 mph. The wind is blowing at a bearing of 135° at a speed of 40 mph. What is the actual velocity of the plane?
b) A 700 lb force just keeps a 4000 lb box from sliding down a ramp. What is the angle of inclination of the ramp?
c) Two tow trucks are pulling on a truck stuck in the mud. Tow truck #1 is pulling with a force of 635 lbs at 51° from the horizontal while tow truck #2 is pulling with a force of 592 lbs at 39° from the horizontal. What is the magnitude and direction of the resultant force?
Explanation / Answer
(A) velocity of plane wrt wind,
vP/W = 400 (cos45i + sin45)
and vW = 40 (cos135 i + sin135j)
vP = vP/W + vW
vP = 254.6 i + 311.1 j
|vP| = sqrt(254.6^2 + 311.1^2) = 402 mph
theta = tan^-1(311.1/254.6) = 50.7 deg
(B) Fnet = 4000 sin(theta) - 700 = 0
theta = sin^-1(700/4000) = 10 deg
(C) Fnet = F1+ F2
= (635cos51 + 592 cos39)i + (635sin51 + 592 sin39)j
= 859.7 i + 866 j
magnitude = sqrt(859.7^2 + 866^2) = 1220 lns
direction = tan^-1(866 / 859.6) = 45.2 deg
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.