Question

)A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 452 km/hour at an altitude of 975 m . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80 m/s2 . What is the speed vf of the package when it hits the ground?

Answer 1

187 m/s

Step-by-step explanation:

Given:

uₓ = 452 km/hr = 125.556 m/s

aₓ = 0 m/s²

sᵧ = -975 m

uᵧ = 0 m/s

aᵧ = -9.80 m/s²

Find: vₓ and vᵧ

Equation: v² = u² + 2as

In the x-direction:

vₓ² = uₓ² + 2 aₓ sₓ

vₓ² = (125.556 m/s)² + 2 (0 m/s²) sₓ

vₓ = 125.556 m/s

In the y-direction:

vᵧ² = uᵧ² + 2 aᵧ sᵧ

vᵧ² = (0 m/s)² + 2 (-9.80 m/s²) (-975 m)

vᵧ = 138.239 m/s

The magnitude of the velocity is:

v² = vₓ² + vᵧ²

v² = (125.556 m/s)² + (138.239 m/s)²

v = 186.75 m/s

Rounded to three significant figures, the final velocity is 187 m/s.