Question

A plane travels 2.5 km at an angle of 35 deg to the ground, then changes direction and travels 5.2 km at an angle of 22 deg to the ground. what is the magnitude and direction of the plane's total displacement?

Answer 1

Alright, lets get started.

Please have a look at the diagram attached.

2.5 km at an angle of 35 deg to the ground.

So, AB = 2.5 sin 35 = 1.4 km

BC = 2.5 cos 35 = 2.0 km

Plane changes direction and travels 5.2 km at an angle of 22 deg to the ground.

DE = 5.2 sin 22 = 1.95 km

AE = 5.2 cos 22 = 4.82 km

Total,

X component =
`CF = BC + AE = 2 + 4.82 = 6.82 km`

Y component =
`DF = AB + DE = 1.4 + 1.95 = 3.35 km`

Net displacement d =
`√(6.82^2+3.35^2)= 7.6 km`

For Angle

tan θ =
`(Y)/( X)= (3.35)/(6.82) = 0.49`

So,

θ =
`tan^(-1)(0.49) =26`

Hence magnitude is 7.6 km and angle is 26 degrees. : Answer

Hope it will help.