Stone dropped from top of a tower 100m high. At same instant another stone is thrown vertically from base of the tower with a velocity of 25m/s. When and where will the two stones meet? Given g =10 m/s^2
stone one:
h=100-1/2 g t^2
stone two:
h=25t-1/2 g t^2
set them equal, solve for time t time of impact.
Wondering why you were told to use g=10? It is nowhere on Earth that value. Do you use PI as 3.0? Goodness, so instructors really think students are so inept they cant use actual values, and are limited to whole numbers?
To find when and where the two stones will meet, we need to determine the time it takes for each stone to reach the meeting point.
First, let's consider the stone dropped from the top of the tower without any initial velocity.
For this stone, the equation of motion is given by:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity, and t is the time.
In this case, h = 100m, g = 10m/s^2, and we need to solve for t.
Substituting the given values into the equation, we get:
100 = (1/2) * 10 * t^2
Simplifying the equation, we have:
10t^2 = 100
Dividing both sides by 10:
t^2 = 10
Taking the square root of both sides:
t = √10 ≈ 3.16 seconds
So, it takes approximately 3.16 seconds for the stone dropped from the top of the tower to reach the meeting point.
Now, let's consider the stone thrown vertically from the base of the tower with an initial velocity of 25m/s.
Since the velocity is in the same direction as the acceleration due to gravity, the stone will be moving downward.
The equation of motion for this stone is given by:
h = (v0 * t) + (1/2) * g * t^2
where h is the height, v0 is the initial velocity, g is the acceleration due to gravity, and t is the time.
In this case, h = 100m, v0 = -25m/s (negative sign indicates downward direction), g = 10m/s^2, and we need to solve for t.
Substituting the given values into the equation, we get:
100 = (-25 * t) + (1/2) * 10 * t^2
Simplifying the equation, we have:
5t^2 - 25t + 100 = 0
Dividing both sides by 5:
t^2 - 5t + 20 = 0
Using the quadratic formula, t = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -5, and c = 20:
t = (-(-5) ± √((-5)^2 - 4*1*20)) / (2*1)
t = (5 ± √(25 - 80)) / 2
t = (5 ± √(-55)) / 2
Since we have a negative number under the square root, this means the stones will not meet at a common point.
Therefore, the two stones will not meet.