Question

A string attached to an airborne balloon was maintained at an angle of 54 degrees with the ground. If 2.3 m of string was reeled in to return the balloon back to the ground, what was the horizontal and vertical displacements

Answer 1

dₓ = 1.35 m

dy = 1.86 m

Step-by-step explanation:

In order to find the vertical and horizontal components of the displacement, we can assume a right triangle. Such that, the length of string is the hypotenuse, making and angle of 54° with the base of triangle. The base is the horizontal component of displacement. And the perpendicular is the vertical component of displacement. Therefore:

`d_(x) = d\ Cos\ \theta`

where,

dₓ = horizontal component of displacement = ?

d = resultant displacement = 2.3 m

θ = angle between displacement and ground = 54°

Therefore,

`d_(x) = (2.3\ m)\ Cos\ 54^0`

dₓ = 1.35 m

For vertical component of displacement:

`d_(y) = d\ Sin\ \theta\\d_(y) = (2.3\ m)\ Sin\ 54^0`

dy = 1.86 m