A boy is standing at the top of the a building, 40 m high. He leans over the side and throws a pebble vertically upwards from the edge of the building at 12m.s^-1. The pebble reaches the ground at the foot of the building. Calculate time for the pebble to reach the ground

To calculate the time it takes for the pebble to reach the ground, we can use a kinematic equation.

First, let's define the known variables:

- Initial velocity (u) = 12 m/s. The pebble is thrown upwards, so the initial velocity has a positive value.
- Final velocity (v) = 0 m/s. The pebble reaches its highest point at the top and then starts falling downwards. At the highest point, its velocity is zero.
- Acceleration (a) = -9.8 m/s². Gravity is acting in the downward direction, so acceleration is negative.
- Displacement (s) = -40 m. The pebble travels a distance of 40 meters downward from the top of the building to the ground. Since it's moving in the opposite direction to the positive direction of the axis, displacement is negative.

Now, using the kinematic equation:

v² = u² + 2as

Substituting the given values:

0² = (12)² + 2(-9.8)(-40)

Simplifying the equation:

0 = 144 + 784

Since the equation does not hold, this means the pebble does not reach the ground. There may be some mistake in the question or insufficient information provided. Please double-check the values or provide any missing details to get the accurate answer.

To calculate the time it takes for the pebble to reach the ground, we can use the equation of motion:

s = ut + (1/2)at^2

Where:
- s is the distance traveled (in this case, 40 m, the height of the building)
- u is the initial velocity (12 m/s, the velocity at which the pebble is thrown upwards)
- a is the acceleration (in this case, -9.8 m/s^2, since the acceleration due to gravity is acting downwards)
- t is the time taken (what we're trying to find)

Since the pebble is thrown upwards and comes to rest at the topmost point, the final velocity (v) will be 0 m/s. Therefore, we can rewrite the equation as follows:

0 = 12 - 9.8t

Solve this equation for t:

9.8t = 12

t = 12 / 9.8

Using a calculator, we can find:

t ≈ 1.2245 seconds

Therefore, it will take approximately 1.2245 seconds for the pebble to reach the ground.