An object is projected vertically in "V" velocity.After "T" time, another object is projected at the same place in same velocity("V").Find the velocities of stones when they meets.
To find the velocities of the two objects when they meet, we need to first analyze their motion separately and then determine the time it takes for them to meet.
Let's consider the motion of the first object:
1. The object is projected with an initial velocity, V, in the upward direction.
2. Assuming no other forces are acting on it, the only force acting on the object is gravity, which causes it to accelerate downward at a rate of 9.8 m/s^2.
3. At any given time, t, the velocity of the first object can be calculated using the equation: v1 = V - 9.8t, where v1 is the velocity of the first object at time t.
Now, let's consider the motion of the second object:
1. The second object is also projected with an initial velocity, V, in the upward direction.
2. Assuming no other forces are acting on it, the only force acting on the object is gravity, which causes it to accelerate downward at a rate of 9.8 m/s^2.
3. However, the second object is projected after time T, so it will take T seconds longer to reach the same height as the first object.
4. Therefore, at any given time, t, the velocity of the second object can be calculated using the equation: v2 = V - 9.8(t - T), where v2 is the velocity of the second object at time t.
To find the time it takes for the two objects to meet, we need to set v1 equal to v2:
V - 9.8t = V - 9.8(t - T)
Simplifying this equation:
V - 9.8t = V - 9.8t + 9.8T
9.8T = 0
T = 0
The equation indicates that the time it takes for the two objects to meet is 0 seconds. This means that they are projected from the same place at the same time, so their velocities will also be the same when they meet.
Therefore, the velocities of the two objects when they meet are both V.
To determine the velocities of the two objects when they meet, we need to take into account their initial velocities and times of projection.
Let's start by considering the vertical motion of the first object. The object is projected vertically upwards with an initial velocity "V".
Using the kinematic equation for vertical motion:
v = u + gt
Where:
v is the final velocity,
u is the initial velocity,
g is the acceleration due to gravity (approximately -9.8 m/s^2),
t is the time.
In this case, the initial velocity (u) is "V" and the time (t) is "T". Plugging in these values, we get:
v1 = V - 9.8T
Now let's consider the second object. It is also projected vertically upwards at the same place with the same initial velocity "V" after time "T". So, the time for the second object is also "T".
Using the same kinematic equation:
v = u + gt
Plugging in the values, we get:
v2 = V - 9.8T
Now, since we want to know the velocities of the two objects when they meet, we can equate v1 and v2 to find the common velocity they both have at that point:
V - 9.8T = V - 9.8T
Simplifying this equation, we can see that the initial velocity "V" cancels out:
-9.8T = -9.8T
This means that the velocities of both objects when they meet will be equal to each other, and they will both have a velocity of -9.8T (negative, indicating motion in the opposite direction of their initial projections).
Therefore, the velocity of both objects when they meet is -9.8 times the time of projection (T).