SOLUTION: A human catapult is used to launch a person into a lake. The height, in feet, of the person is modeled as shown, h(t)=-16t^(2)+50t+20 where t is the time in seconds from the launch

Algebra ->  Coordinate-system -> SOLUTION: A human catapult is used to launch a person into a lake. The height, in feet, of the person is modeled as shown, h(t)=-16t^(2)+50t+20 where t is the time in seconds from the launch      Log On


   

Question 1202374: A human catapult is used to launch a person into a lake. The height, in feet, of the person is modeled as shown, h(t)=-16t^(2)+50t+20 where t is the time in seconds from the launch. Part A What equation can you use to find when the person touches the lake? Find the solution
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

The catapulted person touches the lake when its height is zero.


Therefore, the equation to solve is THIS

    -16t^2 + 50t + 20 = 0.


To solve it, simplify it first

    8t^2 - 25t - 10 = 0,

then apply the quadratic formula

    t%5B1%2C2%5D = %2825+%2B-+sqrt%2825%5E2+-+4%2A8%2A%28-10%29%29%29%2F%282%2A8%29 = %2825+%2B-+sqrt%28945%29%29%2F16.


We deny the negative root and accept the positive root  t = %2825+%2B+sqrt%28945%29%29%2F16 = 3.48 seconds  (rounded).

Solved.

-----------------

To see many other similar solved problems,  look into the lessons
    - Introductory lesson on a projectile thrown-shot-launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform
in this site.

Learn the entire subject from this source.