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).

Answer_____________________

Answer 1

a

x-component
`20 \ m`

y-component
`500 - 452 = 48 \ m`

b

Magnitude
`d = 52 \ m`

direction is
`\theta = 67.4^o`

Step-by-step 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 = √( x- component ^2 + y- component ^2 )`

`d = √( 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)[ (48)/(20)]`

=>
`\theta = tan ^(-1)[ 2.4 ]`

=>
`\theta = 67.4^o`