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2 answers:
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Answer:
Time = 0.55 s
Height = 8.3 m
Explanation:
The ball is dropped and therefore has an initial velocity of 0. Its acceleration, g, is directed downward in the same direction as its displacement, .
The dart is thrown up in which case acceleration, g, acts downward in an opposite direction to its displacement, . Both collide after travelling for a time period, t. Let the height of the dart from the ground at collision be
and the distance travelled by the ball measured from the top be
.
It follows that .
Applying the equation of motion to each body (h = v_0t + 0.5at^2),
Ball:
(since
.)
Dart:
(the acceleration is opposite to the displacement, hence the negative sign)
But
The height of the collision is the height of the dart above the ground, .