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  4. A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following has the same value at the time of throw and the time of return? I. Kinetic energy of the ball II. Speed of the ball III. Vertical component of velocity IV. Horizontal component of velocity

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Q. A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following has the same value at the time of throw and the time of return?
I. Kinetic energy of the ball
II. Speed of the ball
III. Vertical component of velocity
IV. Horizontal component of velocity

Motion in a Plane

Solution:

If we neglect air resistance, horizontal component of velocity is always same.
image
To find vertical component use equation,
$v_f^2=v_i^2-2 g \times h, $
$ v_i=u \sin \theta, h=0$,
$v_f^2=u^2 \sin ^2 \theta-0, v_f=u \sin \theta$
hence $\vec{v}=u \cos \theta \hat{i}-u \sin \theta \hat{j}$
$\therefore$ Speed is same, so K.E. is same.