A physics student kicked a soccer ball toward an aprtment building 40.8 meters from her. The velocity of the ball was 40 m/s^2 @30 degrees. At what approximate height did the ball hit the building?

initial vertical velocity = Vi=40 sin 30 = 20 m/s (not m/s^2)

constant horizontal velocity = 40 cos 30
How long to get there?

40.8 m/(40 cos 30) = 1.18 seconds

so now the vertical problem, how high after 1.18 s
h = Vi t - (1/2) g t^2
h = 20(1.18) -4.9(1.18)^2
all yours :)

To find the approximate height at which the soccer ball hits the building, we can break down the initial velocity into its horizontal and vertical components.

The horizontal component of the velocity remains constant throughout the motion and does not affect the vertical motion of the ball. So, we can ignore the horizontal component for this calculation.

The vertical component of the velocity can be determined using trigonometry. The initial velocity of 40 m/s makes an angle of 30 degrees with the horizontal. To find the vertical component, we can use the formula:

Vertical Component of Velocity = Initial Velocity * sin(theta)

Here, theta is the angle of 30 degrees. So,

Vertical Component of Velocity = 40 m/s * sin(30°)

Now, we can find the time taken by the ball to reach the building using the equation of motion:

Distance = Initial Velocity * time + (1/2) * acceleration * time^2

Since the vertical motion of the ball is affected by gravity, the acceleration is -9.8 m/s^2 (taking downward direction as negative).

Since the ball starts from the ground (height = 0) and reaches a height we need to find, the equation becomes:

Height = (Vertical Component of Velocity) * time - (1/2) * acceleration * time^2

We need to solve this equation to find the time taken for the ball to reach the building.

Substituting the values:

40.8 meters = 20 m/s * sin(30°) * time - (1/2) * (-9.8 m/s^2) * time^2

Simplifying this equation will give you a quadratic equation in terms of time. Once you solve it, you can find the values of time and substitute it back into the equation for height to find the approximate height at which the ball hits the building.