Velocity of a body on reaching the point from which it was projected upwards, is:
A
v=0
B
v=2u
C
v=0.5u
D
v=−u
Step-by-Step Solution
Initial Conditions: A body is projected vertically upwards with an initial velocity u. Let the upward direction be positive (+) and the downward direction be negative (−). Thus, initial velocity is +u.
Displacement Condition: When the body reaches the point of projection, the net displacement (s) is zero because the final position coincides with the initial position.
Apply Kinematic Equation: Use the third equation of motion v2=u2+2as .
Substituting s=0, we get:
v2=u2+2a(0)v2=u2v=±u
Determine Sign: Since the body is moving downwards while returning to the projection point, its velocity must be negative (opposite to the direction of projection). Therefore, the final velocity is v=−u. The magnitude (speed) remains the same, but the direction is reversed .
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