Calculus

posted by .

If an arrow is shot straight up from the surface of the moon with an initial velocity of 100 ft/s, its height in feet after t second is given by s(t)=(100t)−(83/100)(t^2).
Use the limit definition of the derivative to find the answers to the following questions.

Find the velocity of the arrow when t=2.

Find the velocity of the arrow when t=a.

When will the arrow return to the moon's surface?

What will the velocity of the arrow be when it hits the surface?

  • Calculus -

    s(2) = 100(2) - (83/100)(4) = 4917/25
    s(2+h) = 100(2+h) - (83/100)(2+h)^2
    = 200+100h - 332/100 - (332/100)h - (83/100)h^2


    velocity = Limit ( s(2+h) - s(2) )/(2+h - 2) as h -->0
    = Lim (200+100h - 332/100 - (332/100)h - (83/100)h^2 - 4917/25)/h
    = Lim ( (2417/25)h - (83/100)h^2 )/h
    = lim 2417/25 - (83/100)h , as h ---> 0
    = 2417/25 ft/sec

    carefully repeat the above steps using a instead of 2
    you should get
    v(a) = 100 - (83/50) a

    the arrow will return to the surface when s(t) = 0

    100t - (83/100)t^2 = 0
    t (100 - (83/100)t ) = 0
    t= 0 ----> the start of the shot
    or
    t = 100(100)/83 = appr 120.5 seconds

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra

    an arrow is shot into the air with an initial velocity of 96 feet per second. the height in feet of the arrow t seconds after it was shot into the air is given by the function h(x)=-16t^2+96t. find the maximum height of the arrow. …
  2. precal college

    a rocket is shot straight up into the air with an inicial velocity of 250 ft per second and from a height of 100 feet above the ground. h= -16x2+ 250x+ 100
  3. AP Calc. AB

    If an arrow is shot upward on the moon with a velocity of 56 m/s, its height in meters after t seconds is given by . Find the instantaneous velocity after one second.
  4. AP Calc. AB

    If an arrow is shot upward on the moon with a velocity of 57 m/s its height (in meters) after t seconds is given by H= 57t-0.06t^2. With what velocity will the arrow hit the moon?
  5. AP Calc. AB

    1.If an arrow is shot upward on the moon with a velocity of 50 m/s its height (in meters) after t seconds is given by H = 50t - 0.66t2. With what velocity will the arrow hit the moon?
  6. math

    If an arrow is shot straight upward on the moon with a velocity of 73 m/s, its height (in meters) after t seconds is given by s(t) = 73 t - 0.83 t^2. (A) What is the velocity of the arrow (include units) after 5 seconds?
  7. Algebra

    An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function Find the maximum height of the arrow.
  8. Math

    In physics, one learns that the height of an object thrown upward from an initial height of h0 feet with an initial velocity of v0 (in feet per second) is given by the formula h(t)=−16t^2+v0t+h0 feet where t is the amount of …
  9. Maths

    object thrown upward from an initial height of h0 feet with an initial velocity of v0 (in feet per second) is given by the formula h(t)=−16t^2+v0t+h0 feet where t is the amount of time in seconds after the ball was thrown. Also, …
  10. Aria

    If a projectile is shot vertically upward from the ground with an initial velocity of 100 ft per sec, neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by s= -16t^2 + 100t a) After …

More Similar Questions