Calculus

If a rocket is shot vertically upward from the ground with an initial velocity of 192 ft/sec.
a. When does it reach its maximum height above the ground?
b. What is the maximum height reached by the rocket?
c. How long does it take to reach the ground again?
d. At what speed will the rocket hit the ground?

  1. 👍
  2. 👎
  3. 👁
  1. the height h is given by
    h = 192t - 16t^2
    (a,b) find the vertex of the parabola
    (c) solve for t when h=0
    (d) final speed is the same as the starting speed, since momentum is conserved

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    A toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function f(t)=-16t^2+48t , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height. What

  2. calculus

    If a rocket is shot vertically upward from the ground with an initial velocity of 192 ft/sec, when does it reach its maximum height above the ground and what is that maximum height? Also find how long it takes to reach the ground

  3. Physics

    A test rocket is launched vertically from ground level (y=0m), at time t=0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 97 m and

  4. algebra

    A rocket is launched from atop a 76-foot cliff with an initial velocity of 107 ft/s. The height of the rocket above the ground at time t is given by . A) When will the rocket hit the ground after it is launched? Round to the

  1. pyhsics

    A cannonball is shot (from ground level) with an initial horizontal velocity of 36.0 m/s and an initial vertical velocity of 21.0 m/s. 1) What is the initial speed of the cannonball? 2) What is the initial angle θ of the

  2. algebra

    A rocket is shot into the air at a velocity of 48 ft/ sec. The equation is h(t) = -16t^2+48t+4 1) How far off the ground did the rocket start from? 2) Using the quadratic function, how high the rocket will be at its maximum point?

  3. math

    a model rocket is projected straight upward from the ground level. It is fired with an initial velocity of 192 ft/s. How high is the rocket after 10 seconds?

  4. Math

    A rocket is launched from ground level with an initial vertical velocity (v0) of 176 ft/s. After how many seconds will the rocket hit the ground? (Hint: h(t) = -16t2 + v0t + h0)

  1. 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

  2. Physics 11U

    At the moment when a shot putter releases a 5.00 kg shot, the shot is 2.00 m above the ground and travelling at 15.0 m/s. It reaches a maximum height of 8.0 m above the ground and then falls to the ground. Assume air resistance is

  3. Math000

    The height (in meters) of a projectile shot vertically upward from a point 3 m above ground level with an initial velocity of 21.5 m/s is h = 3 + 21.5t − 4.9t2 after t seconds. (Round your answers to two decimal places.) (a)

  4. Physics

    A bullet is fired vertically upward with an initial velocity of 98m/s from the top of a building 100m high, find a) the maximum height reached above the ground b) the total time before reaching the ground. C) the velocity on

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