A ball is projected vertically upward with a velocity of 80m/s. Two seconds later a second ball is projected vertically upward with a velocity of 60m/s. At what point above the surface of earth will they meet?
Let's take the upwards as the positive direction. After the first ball reached the height and its vertical displacement can be written as follows:
Let's find the velocity and height of the first ball after :
Then, we can write the vertical displacement of the second ball projected vertically upward two seconds later:
At the moment when they meet and we can write:
Substituting and in the previous equation, we get:
The time is negative, which means that two balls never meet at the height above the earth.
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