Calculus

A ball is thrown vertically into the air so that its height s after t seconds is given by the equation, s=-1/27(t^2)+4√t. Find its maximum height.

  1. 👍
  2. 👎
  3. 👁
  1. ds/dt = -2/27 t + 2/√t
    = (54-2t^(3/2))/(27√t)

    ds/dt=0 when

    54 - 2t^(3/2) = 0
    t^(3/2) = 27
    t = 9

    now just find s(9)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    THe function h(t)=-16t^2+v0t+h0 describes the height in feet above the ground h(t) of an object thrown vertically from a height of h0 feet, with an initial velocity of v0 feet per second, if there is no air friction and t is the

  2. pre-calc

    Physics: a ball is thrown vertically upward with an initial velocity of 80 feet per second. the distance (in feet) of the ball from the ground after t seconds if s=80t-16tt^2 a) draw the illustration b) for what time interval is

  3. science

    a ball is thrown straight upward and returns to the thrower's hand after 3.00s in the air. A second ball is thrown at an angle of 30.0 deg with the horizontal. At what speed must the second ball be thrown so that it reached the

  4. Algebra

    A ball is thrown into the air. The height h, in feet, of the ball can be modeled by the equation h= -16t^2+20t+6, where t is the time, in seconds, the ball is in the air. When will the ball hit the ground? first should I use x=

  1. algebra

    A ball is thrown into the air with an upward velocity of 40 feet per second. Its height, h, in feet after t seconds is given by the function h(t)=-16t^2+40t+10. a. What is the ball’s maximum height? 35Ft b. When the ball hits

  2. mathematics

    the height of a ball t seconds after it is thrown into the air from the top of the building can be modelled by h(t)= -16t2+48t+64 where h(t) is height in metres.how high is the building? how high does the ball rise before starting

  3. Algebra 1

    a ball is thrown into the air with an upward velocity of 32 ft per second. Its height h in feet after t seconds is given by the function h(t)=-16t^2 +32t+6. How long does it take the ball to reach its maximum height? What is the

  4. math

    A ball is thrown into the air with an upword velocity of 36 ft/s. Its hight H in feet after t seconds is given by the function h=-16t^2+36t+9. In how many seconds does the ball reach its maximum height? Round to the nearest

  1. physics

    A ball is thrown vertically upward with an initial speed of 20 m/s. Two seconds later, a stone is thrown vertically (from the same initial height as the ball) with an initial speed of 24 m/s. At what height above the release point

  2. Calculus 1

    A ball is thrown vertically upward from ground level with initial velocity of 96 feet per second. Assume the acceleration of the ball is a(t) = -32 ft^2 per second. (Neglect air Resistance.) (a) How long will it take the ball to

  3. math

    A ball is thrown into the air with an upward velocity of 48 /. Its height ℎ in feet after seconds is given by the function ℎ = −162 + 48 + 9. How long does it take the ball to reach is the maximum height? What is the

  4. Calculus

    1.if a ball is thrown into the air with a velocity of 35ft/s, it's height in feet after t seconds is given by y=35t-10t^2. Find the averag velocity for the time period beginning when t=4 and lasting 0.05s. 2.if a ball is thrown

You can view more similar questions or ask a new question.