Question

An airplane accelerates at 7.5 m/s2 at an angle of 16° above the horizontal. Find the horizontal and vertical components of the acceleration.

horizontal component: ______ m/s2
vertical component: ______ m/s2

Answer 1

`the \: horizontal \: component \: of \: the \: acceleration : \\ a_(x) = 7.21\: {m(s)}^( - 2) \\ the \: vertical \: component \: of \: the \: acceleration : \\ a_(y) = 2.07 \: {m(s)}^( - 2)`

Step-by-step explanation:

`the \: horizontal \: component \: of \: the \: acceleration : \\ a_(x) = a \: \cos( \alpha ) \\ a_(x) = 7.5 \: \cos(16) \\ a_(x) = 7.2094627195 \: {m(s)}^( - 2) \\ \\ the \: vertical \: component \: of \: the \: acceleration : \\ a_(y) = a \: \sin( \alpha )\\a_(y) = 7.5 \: \sin(16) \\ a_(y) = 2.0672801686 \: {m(s)}^( - 2) \\`

Answer 2

horizontal component:
`7.2\ m/s^2`

vertical component:
`2.1\ m/s^2`

Step-by-step explanation:

Rectangular components of a vector

Given a vector as a (magnitude, angle) pair, the rectangular components can be calculated as:

`a_x= magnitude*cos(angle)`

`a_y=magnitude*sin(angle)`

The acceleration of the airplane is given with a magnitude of 7.5 m/s^2 and an angle of 16°.

Calculate the components:

`a_x=7.5*cos(16^\circ)=7.2\ m/s^2`

`a_y=7.5*sin(16^\circ)=2.1\ m/s^2`

horizontal component:
`7.2\ m/s^2`

vertical component:
`2.1\ m/s^2`