a plane travels 2.5 km at an angle of 35 degrees to the ground and then changes Direction and travels 5.2 km and an angle of 22

Question

4 years ago

13

degrees to the ground what is the magnitude and direction of the Plains total displacement

1 answer:

Bess [88] · Answer 1 · 2021-12-26T19:59:05+03:00

We can solve for the resultant x and y components by using the sine and cosine functions.

resultant x = 2.5 cos 35 + 5.2 cos 22 = 6.87 km

resultant y = 2.5 sin 35 + 5.2 sin 22 = 3.38 km

The resultant displacement is calculated using hypotenuse equation:

displacement = sqrt (6.87^2 + 3.38^2)

displacement = 7.66 km

The resultant angle is:

θ = tan^-1 (3.38 / 6.87)

θ = 26.20°

Therefore the magnitude and direction is:

7.66 km, 26.20° to the ground