SOLUTION: If you throw a rock straight up with an initial velocity of 20 m/s,
a) How high does it travel?
b) How long does it take for the rock to reach its maximum height?
Algebra.Com
Question 234663: If you throw a rock straight up with an initial velocity of 20 m/s,
a) How high does it travel?
b) How long does it take for the rock to reach its maximum height?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The vertical distance as a function of time is given by:
\ =\ -\frac{1}{2}gt^2\ +\ v_ot\ +\ h_o)
where 
m/secē is the acceleration due to gravity, 
m/sec is the initial velocity, and 
is the height of your hand above the ground when you let go of the rock.
First answer part b). To answer part b), realize that the graph of this function is a parabola opening downward with vertex at
\right))
and that
because for a general quadratic function, \ =\ ax^2\ +\ bx\ +\ c)
, the 
-coordinate of the vertex is 
Once you have calculated 
, which is the solution to part b), find the value of the height function for that time, that is:
\ =\ -\frac{1}{2}g(t_{max})^2\ +\ v_ot_{max}\ +\ h_o)
Making the appropriate substitution for based on your personal physical stature and the mechanics of your throwing arm and you will have the solution to part a)
John
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