college algebra

The height of a projectile fired upward is given by the formula s = v0t – 16t2, where s is the height, v0 is the initial velocity and t is the time. Find the times at which a projectile with an initial velocity of 128 ft/s will be 144 ft above the ground. Round to the nearest hundredth of a second.
t = sec (smaller value)
t = sec (larger value)

  1. 👍 1
  2. 👎 0
  3. 👁 1,472
  1. So you are solving:

    144 = 128t - 16t^2

    16t^2 - 128t + 144 = 0
    t^2 - 8t + 9 = 0

    I will complete the square, (in this case faster than the formula)
    t^2 - 8t + 16 = -9+16
    (t-4)^2 = 7
    t-4 = ±√7
    t = 4 ± √7
    I get appr 6.65 and 1.35

    1. 👍 0
    2. 👎 0
  2. h = hi + Vi t - (1/2) g t^2
    in ancient English units this is

    h = Hi + Vi t - (1/2) 32 t^2

    If
    Hi = 0
    Vi = 128 ft/s
    then
    h = 128 t - 16 t^2
    for h = 144
    144 = 128 t - 16 t^2

    16 t^2 - 128 t + 144 = 0

    t^2 - 8 t + 9 = 0

    t = [ 8 +/- sqrt(64 -36) ]/2

    t = 4 +/- sqrt 7

    t = 1.35
    t = 6.65

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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)

  2. physics

    a projectile with a muzzle velocity of 550 m/s is fired from the a gun on top of a cliff 460 m above the sea level at a certain angle with respect to the horizontal. if the projectile hits the ocean surface. 49.2 seconds after

  3. physics

    A projectile is fired with an initial speed of 65.2 m/s at an angle of 34.5 degree above the horizontal on a long flat firing range. Determine (a) The maximum height reached by the projectile, (b) The total time in the air, (c)

  4. pre-calc

    analyzing the motion of a projectile: a projectile is fired from a cliff 200 feet above the water at an inclination of 45 degrees, with a muzzle velocity of 50 feet per second. the height of the projectile above the water is given

  1. physics

    a projectile is fired from the surface of the earth with a speed of 200 m/s at an angle of 30 degrees above the horizontal. If the ground is level, what is the maximum height reached by the projectile

  2. Science

    A projectile has a range of 50m and reaches a maximum height of 10m. Calculate the angle at which the projectile is fired.

  3. Math

    A bullet is fired straight up from a gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula h=−16t2+v0t+8 to determine how many seconds it will take for the bullet to hit the ground. (That

  4. Physics Help

    A projectile is fired at an upward angle of 60 degrees with a speed of 100m/s. It lands on a plateau 150m higher. What is the projectile's speed the moment before it strikes the plateau? I'm thinking to just use the kinematic

  1. Algebra

    A projectile is launched upward with a velocity of 128 feet per second from the top of a 50- foot platform. What is the maximum height attained by the projectile?

  2. Physics

    A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30° above the horizontal. If the ground is level, what is the maximum height reached by the projectile? (A) 5 m (B) 10 m (C)

  3. Math

    11. A rocket is fired upward from some initial height above the ground. Its height h in feet above the ground t seconds after it is fired is given by h = -16t2 + 48t +448. (i) What is its initial height? __________ ft. (ii) What

  4. Physics

    a) A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 100 m above ground level, and the ball is fired with initial horizontal speed v_0. Assume acceleration due to gravity to be g = 9.80 m/s^2.

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