A particle is dropped from a tower .it is found that it travels 45 m i...
**Problem:**
A particle is dropped from a tower. It is found that it travels 45 m in the last second of its journey. Find out the height of the tower.
**Solution:**
To find out the height of the tower, we can use the following formula:
h = 1/2 * g * t^2
Where h is the height of the tower, g is the acceleration due to gravity (9.8 m/s^2) and t is the time taken for the particle to fall from the tower.
We know that the particle travels 45 m in the last second of its journey. This means that it takes 1 second to travel the last 45 m. Therefore, the total time taken for the particle to fall from the tower can be calculated as follows:
t = 1 + x
Where x is the time taken by the particle to fall from the tower up to the last second.
Now, we need to find out the value of x. We know that the particle falls under the influence of gravity, which means that its velocity increases by 9.8 m/s every second. Therefore, we can use the following formula to find out the velocity of the particle at the end of x seconds:
v = g * x
We also know that the particle travels 45 m in the last second of its journey. Therefore, the distance traveled by the particle in the first x - 1 seconds can be calculated as follows:
d = 1/2 * g * (x - 1)^2
Now, we can use the following formula to find out the value of x:
45 = v + 1/2 * g * (x - 1)^2
Substituting the value of v in the above equation, we get:
45 = g * x + 1/2 * g * (x - 1)^2
Simplifying the equation, we get:
x^2 - x - 90 = 0
Solving the above equation, we get:
x = 10 or x = -9
Since x cannot be negative, we can discard the value of x = -9. Therefore, the value of x is 10 seconds.
Now, we can use the formula for height to find out the height of the tower:
h = 1/2 * g * t^2
Substituting the values of g and t, we get:
h = 1/2 * 9.8 * 10^2
Simplifying the equation, we get:
h = 490 m
Therefore, the height of the tower is 490 m.
**Conclusion:**
The height of the tower is 490 m.
A particle is dropped from a tower .it is found that it travels 45 m i...
For calculating height of the tower first of all we will have to calculate the total time of flight,let the total time taken be n seconds.
Distance travelled in last second
S = u + a(n - 1/2)
45 = 0 + 10(n - 1/2)
n = 4.5 + 0.5
n = 5th second
So,total time of flight is 5 seconds
Height of the tower
H = 0.5gt^2
= 0.5 × 10 × 5^2
= 125 m
SO THE HEIGHT OF THE TOWER IS 125m
# NOTE:
distance travelled in n seconds:
S1= un + 1/2a(n^2)
distance travelled in (n-1) seconds:
S2 = u(n-1) + 1/2a((n-1)^2)
distance travelled in nth second:
S1-S2= u + 1/2a(2n-1)