A heavy stone is thrown from a cliff of height h with a speed v. The stone will hit the ground with maximum speed if it is thrown
(a) vertically downward
(b) vertically upward
(c) horizontally
(d) the speed does not depend on the initial direction
Concept of Physics - 1 , HC VERMA , Chapter " Work and Energy"
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Answer ⇒ Option (d).
The speed does not depends upon the Initial Position.
Explanation ⇒
Let the stone or any object is thrown upwards, Thus the total mechanical energy will be equal to the sum of the kinetic energy and the Potential Energy.
∴ Total Mechanical Energy = Kinetic Energy +Potential Energy.
= ½mv² + mgh.
Now, This energy is totally conserved (assuming zero friction) and when it will near the earth's surface, the Potential energy will also be converted to Kinetic energy because of height at that point will be 0.
Suppose if the body hits the surface with speed v',then
its total mechanical energy = ½mv'²
Now, From the above, we get,
½mv'²=½mv²+mgh
m(v'²) = (v²+2gh)
Now, v' depends only on the value of v whatever be the initial direction.
Hence, Option d is correct.
Hope it helps.
The speed does not depends upon the Initial Position.
Explanation ⇒
Let the stone or any object is thrown upwards, Thus the total mechanical energy will be equal to the sum of the kinetic energy and the Potential Energy.
∴ Total Mechanical Energy = Kinetic Energy +Potential Energy.
= ½mv² + mgh.
Now, This energy is totally conserved (assuming zero friction) and when it will near the earth's surface, the Potential energy will also be converted to Kinetic energy because of height at that point will be 0.
Suppose if the body hits the surface with speed v',then
its total mechanical energy = ½mv'²
Now, From the above, we get,
½mv'²=½mv²+mgh
m(v'²) = (v²+2gh)
Now, v' depends only on the value of v whatever be the initial direction.
Hence, Option d is correct.
Hope it helps.
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