A baseball is projected horizontally from the top of a building with an initial speed of 15 m/s. The ball strikes the ground 25 m from the base of the building.
a. How long will it be in the air?
b. How tall is the building?
L=v(x)t
t=L/v(x) =25/15=1.67 s
h=gt²/2=9.8•1.67²/2=13.6 m
To find the answer to these questions, we can use the equations of motion for projectile motion. The key idea is that the horizontal and vertical motions are independent of each other.
a. How long will it be in the air?
The horizontal motion of the baseball is at a constant speed of 15 m/s. The horizontal distance traveled (range) can be found using the formula:
Range = Initial horizontal velocity * Time
In this case, the Range is given as 25 m and the initial horizontal velocity is 15 m/s. We can rearrange the formula to solve for Time:
Time = Range / Initial horizontal velocity
Substituting the given values into the equation, we get:
Time = 25 m / 15 m/s = 1.67 s
Therefore, the baseball will be in the air for approximately 1.67 seconds.
b. How tall is the building?
To find the height of the building, we need to consider the vertical motion of the baseball. We can use the following equation of motion:
Vertical displacement = Initial vertical velocity * Time + 0.5 * Acceleration due to gravity * Time^2
The initial vertical velocity is zero because the baseball is projected horizontally. The acceleration due to gravity is approximately 9.8 m/s^2. The time is the same value calculated in part a, which is 1.67 s. We can rearrange the equation to solve for the vertical displacement:
Vertical displacement = 0.5 * Acceleration due to gravity * Time^2 = 0.5 * 9.8 m/s^2 * (1.67 s)^2 = 13.025 m
Therefore, the height of the building is approximately 13.025 meters.