A rock thrown straight up with a velocity of

30 m/s from the edge of a building just misses
the building as it comes down. The rock is
moving at 47 m/s when it strikes the ground.
How tall was the building? The accelera-
tion of gravity is 9.8 m/s2 .
Answer in units of m.

Equate energies:

Initial kinetic energy = (1/2)mu²
Final kinetic energy = (1/2)mv²
Potential energy = mgh = (1/2)m(v²-u²)
Solve for h

To find the height of the building, we can use the kinematic equations of motion. The key information we have is the initial velocity of the rock thrown upwards, the final velocity when it strikes the ground, and the acceleration due to gravity.

Let's break down the problem step by step:

Step 1: Find the time taken for the rock to reach its maximum height.

The initial velocity (u) of the rock is 30 m/s, and the acceleration due to gravity (a) is -9.8 m/s² (negative because the acceleration opposes the motion). The final velocity (v) at the maximum height is 0 m/s (because the rock momentarily stops before falling down). We need to find the time (t) taken to reach this point.

We can use the following equation of motion:

v = u + at

Rearranging the equation to solve for time:

0 = 30 m/s + (-9.8 m/s²) * t

30 m/s = 9.8 m/s² * t

t = 30 m/s / 9.8 m/s²

t ≈ 3.06 s

Step 2: Find the maximum height reached by the rock.

We can use the following equation of motion:

v² = u² + 2as

Since the rock momentarily stops at the maximum height, the final velocity (v) is 0 m/s. The initial velocity (u) is 30 m/s, and the acceleration (a) is -9.8 m/s². We need to find the displacement (s) or maximum height.

0 = (30 m/s)² + 2 * (-9.8 m/s²) * s

900 m²/s² = -19.6 m/s² * s

s = 900 m²/s² / -19.6 m/s²

s ≈ -45.92 m

Since we are looking for the height, which cannot be negative, we take the absolute value of the result:

s ≈ 45.92 m

Therefore, the maximum height reached by the rock is approximately 45.92 meters.

Step 3: Find the height of the building.

The height of the building is equal to the maximum height reached by the rock.

Therefore, the height of the building is approximately 45.92 meters.

To determine the height of the building, we can use the kinematic equations of motion.

Let's break down the problem and identify the given information:

Initial velocity (Upwards) = 30 m/s
Final velocity (Downwards) = -47 m/s (negative because it's moving downwards)
Acceleration (Due to gravity) = -9.8 m/s^2 (negative as it opposes the upward motion)

We need to find the height of the building, which is the distance traveled by the rock.

First, let's find the time it takes for the rock to reach the maximum height (when its velocity becomes zero). We can use the equation:

v_f = v_i + a * t

0 m/s = 30 m/s - 9.8 m/s^2 * t

Rearranging the equation to solve for time (t):

9.8 m/s^2 * t = 30 m/s

t = 30 m/s / 9.8 m/s^2 ≈ 3.06 s

Now, let's find the maximum height (H). We can use the equation:

H = v_i * t + (1/2) * a * t^2

H = 30 m/s * 3.06 s + (1/2) * (-9.8 m/s^2) * (3.06 s)^2

H = 91.8 m - 44.9908 m

H ≈ 46.81 m

Therefore, the height of the building is approximately 46.81 meters.