SOLUTION: An object is propelled vertically upward from the ground with an initial velocity of 35 meters per second. Write the equation. When will the object be 25 meters above the ground? W

In this problem, we take the gravity acceleration equal to  10 m/s^ (by rounding the true value of 9.81 m/s^2).


Then the equation for the height is  

    h(t) = -5t^2 + 35t.


To answer first question, solve the equation

    -5t^2 + 35t = 25.


It is equivalent to

    5t^2 - 35t + 25 = 0,  or

     t^2 -  7t + 5  = 0

      =  =  = 


There are two time moments  

     =  = 0.8 seconds (rounded) moving up  and  

     =  = 6.2 seconds (rounded) moving down.




To answer the second question, you need solve this equation

    -5t^2 + 35t = 0.


Factor left side

    -5t*(t-7) = 0


and get the root  t = 7.  So, an object will hit ground in 7 seconds.




To answer the third question, notice that the parabola has the maximum at the midpoint between its y-intersections,

that are 0 and 7.


So, the maximum height is achieved at t=  = 3.5 seconds,

and the maximum height is


    h(7.5) = -5*3.5^2 + 35*3.5 = 61.25 meters.