Acoin is tossed upward from an initial height of 9 m above the ground, with an initial speed of 8.5 m/s m/s. the magnitude of the gravitational acceleration g = 9.8 m/s2 take the point of release to be y0 = 0. choose upward as positive y direction. pay attention to the signs of position, velocity and acceleration. keep 2 decimal places in all answers. (a) find the coin’s maximum height in meters above the ground?

h= 12.68 m  : Maximum height that the coin reaches from the ground.

Explanation:

Kinematic equations to describe the movement of the coin :

In vertical upward movement, the acceleration due to gravity makes sense opposite to displacement, then, g is negative in the equations:

Look at the attached graphic

Vf = Vo - g*t  Formula (1)

Vf² = Vo² - 2*g*y  Formula (2)

Vf : Final speed , Vf=0 at position y

Vo : Initial speed , Vo=8.5 m/s (positive)

g : Acceleration due to gravity , g = 9,8 m/s² (negative)

y: Position to Vf=0 , from an initial height of 9 m above the ground

Calculation of the time (t) in which the currency reaches the height y :(Look at the attached graphic)

We replace data in formula (1)

0=8.5 - 9.8*t

9.8*t = 8.5

t = 8.5/9.8=0.867 s

Calculation of y for the time t at which the final velocity (Vf) is equal to zero:

We replace data in formula (2)

0 = 8.5² - 2*9.8*y

2*9.8*y= 8.5²

y= 8.5²/19.6 =3.68m

Calculation of the maximum height (h) that the coin reaches

(Look at the attached graphic)

h= 9+y

h= 9+3.68 = 12.68 m

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.