# A helicopter goes straight up 500m from a landing pad. It then goes north 20m. Then it goes down 452m. a) What is the displacement of the he

Question

A helicopter goes straight up 500m from a landing pad. It then goes north 20m. Then it goes down 452m. a) What is the displacement of the helicopter?
Express as components of a vector.
x-component_____________________
y-component_____________________

b) What is the displacement of the helicopter? Express as a vector (magnitude and direction).

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2 years 2021-08-06T15:31:04+00:00 1 Answers 5 views 0

a

x-component             $$20 \ m$$

y-component     $$500 – 452 = 48 \ m$$

b

Magnitude $$d = 52 \ m$$

direction is  $$\theta = 67.4^o$$

Explanation:

From the question we are told that

The first  vertical distance is  $$y_1 = 500 \ m$$

The  first horizontal distance  is  $$x = 20 \ m$$

The  second vertical distance is  $$y_2 = 452 \ m$$

Generally the displacement is

x-component             $$20 \ m$$

y-component     $$500 – 452 = 48 \ m$$

Generally the helicopters displacement is mathematically evaluated as

$$d = \sqrt{ x- component ^2 + y- component ^2 }$$

$$d = \sqrt{ 20t ^2 + 48 ^2 }$$

$$d = 52 \ m$$

The  direction is the angle the displacement of the helicopter makes with the horizontal which is mathematically evaluated as

$$\theta = tan ^{-1}[ \frac{48}{20}]$$

=>       $$\theta = tan ^{-1}[ 2.4 ]$$

=>      $$\theta = 67.4^o$$