If the ball leaves the projectile launcher at a speed of 2.2 m/s at an angle of 30ᴼ, and the projectile launcher is on a table at a height of 1.1 m, how far horizontally will it hit the ground?

1.12 m

Explanation:

This situation is related to parabolic motion, hence we can use the following equations:

(1)

(2)

Where:

is the ball final height (when it hits the ground)

is the ball initial height

is the initial velocity

is the angle at which the ball was launched

is the time

is the acceleration due gravity

is the horizontal distance the ball travels

Rewriting (1) with the given values:

(3)

Multiplying all the eqquation by -1 and rearranging:

(4)

So, since we have a quadratic equation here (in the form of,  we will use the quadratic formula to find  :  

  (5)

Where , ,  

Substituting the known values and choosing the positive result of the equation, we have:  

(6)

Now, substituting (6) in (2):

(7)

(8) This is the horizontal distance at which the ball hits the ground.

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.