Question

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

Answer 1

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.