A man stands on the roof of a 10.0 -tall building and throws a rock with a velocity of magnitude 30.0 at an angle of 34.0 above the horizontal. You can ignore air resistance.

Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.

Dimensions must be provided with numbers. That is Thing One to learn about physics.

To calculate the horizontal distance from the base of the building to the point where the rock strikes the ground, we need to split the initial velocity of the rock into its horizontal and vertical components.

Given:
Initial velocity magnitude (v) = 30.0 m/s
Launch angle (θ) = 34.0°
Height of the building (h) = 10.0 m
Acceleration due to gravity (g) = 9.8 m/s²

Step 1: Find the horizontal component of velocity (Vx).
The horizontal component can be calculated using the formula:
Vx = v × cos(θ)
where v is the initial velocity magnitude and θ is the launch angle.

Vx = 30.0 × cos(34.0°)
Vx ≈ 24.80 m/s

Step 2: Find the time of flight (t) for the rock to hit the ground.
The time of flight can be calculated using the formula:
t = (2 × Vy) / g
where Vy is the vertical component of velocity, which can be calculated using the formula:
Vy = v × sin(θ)

Vy = 30.0 × sin(34.0°)
Vy ≈ 16.18 m/s

t = (2 × 16.18) / 9.8
t ≈ 3.31 s

Step 3: Calculate the horizontal distance (d) traveled by the rock.
The horizontal distance can be calculated by multiplying the horizontal component of velocity (Vx) by the time of flight (t):
d = Vx × t

d = 24.80 × 3.31
d ≈ 82.01 m

Therefore, the horizontal distance from the base of the building to the point where the rock strikes the ground is approximately 82.01 meters.