Hypothetically, if you were standing on the balcony of an apartment on the 10th level of building and you throw a ball at 30° above the horizontal away from the building at 4.5m/s, how far from the building would the ball land?. The height from which the ball is thrown is approximately 30m.

Hypothetically, do you ignore wind and air resistance?

Initial vertical velocity: 4.5sin30

go to the height equation:
hf=hi+InitialVelocityvertical*t-1/2 g t^2
hf=-30, hi=0 solve for time in air, t.

distance equation
horizonaldistance= 4.5cos30*timeinair
Hypothetically, with no air friction or force.

First of all your initial vertical velocity is not 4.5 m/s.

it is Viy= 4.5 * sin(30)
and your horizontal = 4.5 * cos(30)

To determine the distance at which the ball would land from the building, we can break down the problem into horizontal and vertical components.

First, let's calculate the time it takes for the ball to hit the ground. Since we know the initial vertical velocity of the ball is 4.5 m/s and the height from which it is thrown is approximately 30m, we can use the kinematic equation:

s = ut + (1/2)at^2

Where:
s = displacement (height) = -30m (negative because it is downward)
u = initial vertical velocity = 4.5 m/s
a = acceleration due to gravity = -9.8 m/s^2 (negative because it acts downward)
t = time

Substituting the values into the equation, we get:

-30 = 4.5t + (1/2)(-9.8)t^2

Simplifying the equation, we have:

-4.9t^2 + 4.5t - 30 = 0

Now, we can solve this quadratic equation for the positive value of t, which will give us the time it takes for the ball to hit the ground.

Once we have the time, we can calculate the horizontal distance traveled by the ball using the horizontal component of the initial velocity, which is given by 4.5 m/s times the cosine of the launch angle (30 degrees).

Now, let's solve the equation:

-4.9t^2 + 4.5t - 30 = 0

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

Where:
a = -4.9
b = 4.5
c = -30

Substituting the values into the formula, we have:

t = (-4.5 ± √(4.5^2 - 4(-4.9)(-30))) / (2(-4.9))

After evaluating the equation, we find two possible values for t. Discard the negative value since it doesn't make sense in this context.

Now that we have the value of t, we can calculate the horizontal distance traveled by the ball using the formula:

distance = horizontal velocity × time

Where:
horizontal velocity = 4.5 m/s × cos(30°)
time = the positive value of t we found earlier

Substituting the values into the equation, we can calculate the distance at which the ball would land from the building.