SOLUTION: Mark's football is stuck in a tree. He hopes to dislodge it by standing on a small hill and throwing a baseball at it. Use the fact that a dropped object falls a distance of 4.9t2

Question 24191: Mark's football is stuck in a tree. He hopes to dislodge it by standing on a small hill and throwing a baseball at it. Use the fact that a dropped object falls a distance of 4.9t2 meters in t seconds. Mark throws the baseball with an initial vertical velocity of 14.7 m/s from a height of 3m.
A. What maximum height does the baseball reach?
B. If the football is 12m above the ground, at what time(s) could the baseball hit it?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
When Mark throws the baseball up, only the vertical part of the velocity he
gives it counts, because the horizontal part just moves the ball sideways
14.7t is his vertical throwing velocity times the time at any point in the baseball's trajectory.
4.9t^2 is the downward velocity due to falling (gravity)
this is the equation:

this is the equation for vertical height in meters. Note that when h = 3,
the height is zero, as it should be.
plugging in 1 sec for t, I get the same answer for h that I get
when I plug in 2 sec.
That means that the baseball is the same height on the way up at 1 sec as it
is on the way down in 2 sec.
That means it reaches the max height in the middle, or 1.5 sec.
plug 1.5 into the equation and that will give you the max height.

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