A girl is standing on top of a roof and throws a rock at 30 m/s at an angle of 30 Degrees below the horizontal If the roof is 50 m high how far from the base of the building will the rock land The answer is 52.3
To find how far from the base of the building the rock will land, we can break down the initial velocity of the rock into its horizontal and vertical components.
The horizontal component of the velocity is 30 m/s * cos(30°) = 25.98 m/s
The vertical component of the velocity is 30 m/s * sin(30°) = 15 m/s
Now, we can use the vertical motion equation to find the time it takes for the rock to reach the ground:
h = (1/2) * g * t^2
50 = (1/2) * 9.8 * t^2
t = sqrt(100/9.8) = sqrt(10.2) = 3.2 seconds
Now, we can use the horizontal motion equation to find how far the rock will land:
d = v * t
d = 25.98 m/s * 3.2 s = 83.1 meters
Therefore, the rock will land 83.1 meters away from the base of the building.