A drone is ascending vertically at a constant speed of $5 \text{ m s}^{-1}$ . When it is at a certain height above the ground, a small package gets detached from it. If the package takes $6 \text{ s}$ to strike the ground, what was the height of the drone at the instant the package was detached?
(Take $g = 10 \text{ m s}^{-2}$ )

Question

A drone is ascending vertically at a constant speed of

5 \text{ m s}^{-1}

. When it is at a certain height above the ground, a small package gets detached from it. If the package takes

6 \text{ s}

to strike the ground, what was the height of the drone at the instant the package was detached?
(Take

g = 10 \text{ m s}^{-2}

)

Quantrex Academy · Accepted Answer

Correct answer: B. 150 m

When the package is detached from the drone, it acquires the initial velocity of the drone.

Initial velocity of the package,

u = 5 \text{ m s}^{-1}

(upwards)

Time taken to reach the ground,

t = 6 \text{ s}

Acceleration due to gravity,

a = -10 \text{ m s}^{-2}

Let the height of the drone at the instant of detachment be

h

. The displacement of the package when it strikes the ground is

s = -h

.

Using the second equation of motion,

s = ut + \dfrac{1}{2}at^2

:

-h = 5 \times 6 + \dfrac{1}{2}(-10)(6)^2

-h = 30 - 5 \times 36

-h = 30 - 180

-h = -150

h = 150 \text{ m}

Answer:

150 \text{ m}

A drone is ascending vertically at a constant speed of 5 m s^ -1 ....