a stone is drop from the top of a building and at thesame time a second stone is thrown vertically upward from the botom of the building at a speed of 20m/s, they passed each other 3s later. find the hight of the building.
Newton's law of motion wrt to displacement:
d=v_i * t + 0.5*a*t^2
For the stone being dropped from building:
a=accerlation=gravity=9.81m/s^2
d=0+0.5*(9.81)*3^2
For the second stone being thrown up vertically:
d=20*3+0.5*(-9.81)*3^2
Since displacement/height is same at 3 seconds:
d-0.5*(9.81)*3^2 = 20*3+0.5*(-9.81)*3^2
Solve for d
so the increase in speed of the dropped one cancels the slow down of the other and
height = initial speed up * time
= 20*3 = 60
To find the height of the building, we need to break down the problem into two parts: the free fall motion of the stone dropped from the top of the building, and the upward motion of the stone thrown vertically from the bottom.
Let's analyze each part separately:
1. Stone dropped from the top of the building:
- We know that the acceleration due to gravity is approximately 9.8 m/s^2 (assuming no air resistance).
- The time taken for the stone to pass the person at the bottom is 3 seconds.
- Thus, the stone's time of flight is also 3 seconds since they pass each other at the same moment.
- We can use the formula for free fall motion: h = (1/2) * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time.
- Plugging in the values, we get: h = (1/2) * (9.8 m/s^2) * (3 s)^2.
- Calculating this, we find that the height of the building based on the stone dropped from the top is h = 44.1 m.
2. Stone thrown vertically upward from the bottom:
- The initial velocity of the stone thrown upward is 20 m/s.
- Since the stone passes the person at the bottom after 3 seconds, we can calculate how high it reached using the formula: h = v_i * t + (1/2) * g * t^2, where v_i is the initial velocity, g is the acceleration due to gravity, and t is the time.
- Plugging in the values, we get: h = (20 m/s) * (3 s) + (1/2) * (9.8 m/s^2) * (3 s)^2.
- Evaluating this, we find that the height reached by the stone thrown upward is h = 144.9 m.
Finally, to find the total height of the building, we need to add the heights calculated from both parts:
Total height of the building = h(top stone) + h(bottom stone)
= 44.1 m + 144.9 m
= 189 m.
Therefore, the height of the building is approximately 189 meters.