A ball is thrown vertically upward from top of a building with speed of 20m/s. On the way back ball misses the building and lands on the ground.

Total time the ball is in air is 6 seconds. Determine the height of the building.

hf=hi+vi*t-4.9t^2 you are given hf as zero, vi as 20, and t is 6. Solve the equation for hi

To determine the height of the building, we can use the laws of motion. Let's break down the problem step by step.

Step 1: Find the time it takes for the ball to reach its highest point.
Since the ball is thrown vertically upward, its initial velocity is positive (+20 m/s) and it decelerates until it reaches its highest point where its velocity becomes zero.

We can use the equation: v = u + at, where:
- v is the final velocity (zero at the highest point),
- u is the initial velocity (20 m/s), and
- a is the acceleration due to gravity (-9.8 m/s^2).

Rearranging the equation, we have: t = (v - u) / a.

Substituting the given values:
t = (0 - 20) / -9.8 = 2.04 seconds.

Therefore, it takes the ball 2.04 seconds to reach its highest point.

Step 2: Find the time it takes for the ball to fall back down from its highest point.
The time it takes for an object to fall freely from a certain height h can be found using the equation: h = (1/2)gt^2, where:
- h is the height (unknown),
- g is the acceleration due to gravity (9.8 m/s^2), and
- t is the time taken (unknown).

Since the ball was already in the air for a total of 6 seconds, we need to subtract the time it took to reach the highest point from this.

t = 6 - 2.04 = 3.96 seconds.

Therefore, it takes the ball 3.96 seconds to fall back down to the ground from its highest point.

Step 3: Calculate the height of the building.
The height of the building is equal to the distance the ball traveled during its upward journey. This can be found using the equation: h = ut + (1/2)at^2, where:
- h is the height (unknown),
- u is the initial velocity (20 m/s),
- t is the time taken to reach the highest point (2.04 seconds), and
- a is the acceleration due to gravity (-9.8 m/s^2).

h = 20 * 2.04 + (1/2) * -9.8 * (2.04)^2
h = 40.8 - 19.7952
h = 21.0048 meters

Therefore, the height of the building is approximately 21.0048 meters.