A body is thrown vertically upward such that it returns to the point o...
Explanation:
When a body is thrown vertically upward, it moves under the influence of gravity. The motion of a body under the influence of gravity is called projectile motion.
Let's consider the following variables:
- u: initial velocity of the body
- v: final velocity of the body
- a: acceleration due to gravity, which is always downward (9.8 m/s^2 in SI units)
- t: time taken by the body to return to the point of projection
- h: maximum height reached by the body above the point of projection
Using the equations of motion, we can relate these variables as follows:
v = u - at (since the body is moving upward, the final velocity is zero)
t = 2u/a (since the body takes the same time to go up and come down)
h = ut - 1/2at^2 (this is the formula for the maximum height reached by the body)
Solution:
Given that the body returns to the point of projection after 8 seconds. Thus, the time taken for the body to reach the maximum height is half of that, which is 4 seconds.
Using the second equation of motion, we can find the initial velocity of the body:
t = 2u/a
4 = 2u/9.8
u = 19.6 m/s
Now, using the third equation of motion, we can find the maximum height reached by the body:
h = ut - 1/2at^2
h = 19.6*4 - 1/2*9.8*(4)^2
h = 78.4 - 78.4
h = 0
Therefore, the maximum height reached by the body above the point of projection will be zero. This means that the body will only reach the point of projection and then fall back down without going any higher.
A body is thrown vertically upward such that it returns to the point o...
80 meter
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