A girl standing on top of a roof Throws a rock at 30m/s at an angle 30 degrees below the horizontal. If the roof top is 50m high, how far from the base of the building with the rock land. The answer is 52.3
To solve this problem, we need to break down the initial velocity of the rock into horizontal and vertical components.
Given:
Initial velocity (v) = 30 m/s
Angle below horizontal (θ) = 30 degrees
Height of the building (h) = 50m
The horizontal component of the initial velocity can be found using trigonometry:
Horizontal component = v * cos(θ)
Horizontal component = 30 * cos(30)
Horizontal component = 30 * √3 / 2
Horizontal component = 15√3
The vertical component of the initial velocity can be found similarly:
Vertical component = v * sin(θ)
Vertical component = 30 * sin(30)
Vertical component = 30 * 1 / 2
Vertical component = 15
Now, we can use the kinematic equation to find the time taken for the rock to reach the ground:
h = (1/2) * g * t^2
50 = (1/2) * 9.8 * t^2
t^2 = 10 / 9.8
t = √(10 / 9.8)
t = √1.02
t = 1.01 seconds
Now, we can find the horizontal distance traveled by the rock:
Horizontal distance = Horizontal component * Time
Horizontal distance = 15√3 * 1.01
Horizontal distance = 15√3 * 1.01
Horizontal distance ≈ 52.3m
Therefore, the rock lands approximately 52.3m from the base of the building.