Un avión que vuela a 70 m/s deja caer una caja de provisiones. ¿Qué distancia horizontal recorrerá la caja antes de tocar el suelo, 340 m más abajo?

The distance is 583.1 m

Explanation:

I will solve it in English, you can translate this if you need.

This question can be translated to:

A plane that flies at 70m/s drops a box of provisions.

What is the horizontal distance that the box travels before touching the ground, 340m under it?

I will solve it in English

The acceleration of the box is a(t) = -9.8m/s^2 j, the minus sign is because the gravity acceleration points downwards.

where j stands for the y-axis, and I for the x-axis.

the velocity of the box can be obtained by integrating that:

v(t) = (-9.8m/s^2)*tj + c*j + k*i

where c is the initial velocity in y, in this case is 0 because the box is dropped, and k is the initial velocity in x, in this case is 70m/s.

So v(t) = (-9.8m/s^2)*t*j +70m/s*i

integrating again, we can find the positions of x and y  

x(t) = 70m/s*t + C

y(t) = (-4.9m/s2)*t^2 + H

Where C and H are the initial positions in X and Y. Suppose that the initial position in X is 0, and the initial position in Y is 340m, so we have:

y(t) =  (-4.9m/s2)*t^2 + 340m

the box reaches the floor at the time where y(t) = 0 =  (-4.9m/s2)*t^2 + 340m

340m = (-4.9m/s2)*t^2

t = √(340/4.9) = 8.33s

Now, we put this time in the equation of X(t) to find the horizontal distance:

X(8.33s) = (70m/s)*8.33s = 583.1m

he made 11 calls in one day

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.