Question

Need 100 IQ and more

Answer 1

Answer:

a. The speed of the helicopter at the moment the package is dropped is approximately 15.519 m/s

b. The position of the package 2s after it is dropped is (31.038 m, -9.8 m)

c. The time of flight of the food package is approximately 5.105 seconds

d. The horizontal distance covered is approximately 79.22 m

Explanation:

The given parameters are;

The height at which the helicopter is flying = 125 m

The magnitude of the velocity of the package after 2 seconds, v = 25 m/s

a. The vertical velocity of the package, $v_y$, is given as follows;

$v_y$ = $u_y$ + g·t

Where;

$u_y$ = 0 m/s for the dropped food package

t = The duration of the package in the air = 2 s

g = The acceleration due to gravity = 9.8 m/s²

Therefore;

$v_y$ = g·t = 9.8 m/s² × 2 s = 19.6 m/s

We have,  $v = \sqrt{v_x^2 + v_y^2}$,

Where;

vₓ = The horizontal velocity of the food package = The horizontal speed of the helicopter

therefore, $v_x = \sqrt{v^2 - v_y^2}$, which gives;

$v_x = \sqrt{v^2 - v_y^2} = \sqrt{25^2 - 19.6^2} \approx 15.519 \ m/s$

The speed of the helicopter at the moment the package is dropped ≈ 15.519 m/s

b. The vertical if the package after 2 s is given as follows;

The vertical position of the package after 2 s is given by the kinematic equation, h = 1/2·g·t² = 1/2 × 9.8 m/s² × 2 s = 9.8 m

The food package is located 9.8 m vertically below the point where it is dropped

The horizontal position, x, of the package after 2 s is given by the following kinematic equation, x = vₓ × t

Therefore, x = 15.519 m/s × 2 s ≈ 31.038 m

The coordinates of the location of the package 2 seconds after it is dropped is (31.038 m, 9.8 m)

c. The time of flight, $t_{tot}$, of the food package which is the time it takes the package to reach the ground from 125 m, is given as follows;

$t_{tot} = \sqrt{\dfrac{2 \cdot h}{g} } = \sqrt{\dfrac{2 \times 125 \ m}{9.8 \ m/s^2} } \approx 5.051 \ seconds$

The time of flight of the food package, $t_{125}$ ≈ 5.105 seconds

d. The horizontal distance covered, $x_{tot}$ = vₓ × $t_{tot}$ ≈ 15.519 m/s × 5.105 s = 79.224495 m ≈ 79.22 m.