Delivery drone approaches a customer's porch flying at 8.65 m above the porch at 21.5 km/hr. (a) at what horizontal distance from the desired landing spot should it release a package? (b) at what speed will the package hit the porch?

(a)

(b)

Explanation:

Horizontal Launching

When an object is released from certain height h with a (only) horizontal speed vo, it describes a curved trajectory with a constant speed in the horizontal direction and a variable speed in the vertical direction, constantly changed by the acceleration of gravity. Their equations are

The distances traveled in both directions are

(a)

The package dropped by the drone will land when it travels down all its initial height, thus the flight time must comply:

Solving for :

The data is: h=8.65 m, v_o=21.5 Km/h = 5.972 m/s

Thus, the horizontal distance is

(b)

The horizontal speed at landing time is (constant)

The vertical speed is

The magnitude of the total speed is

0.19 m/s and 0.45 m/s