Quadratics

The path of a bottle rocket being launched into the air and falling back to the ground can be modeled by the equation s=1/2 at^2+v_o t+s_o where s is the height of the object, a is the acceleration, vo is the initial velocity, and so is the initial height. For one launch, the following measurements were taken at t = 0.5 second the height was measured as 144 feet, at t = 1 second the height was 152 feet, and at t = 2.5 seconds the height was 128 feet. Use this information to answer the following questions.
What was the initial velocity of the rocket?
What was the initial height of the rocket?
What was the acceleration?
What was the maximum height the rocket reached?
When did the rocket hit the ground?

I am at a loss on how to get started.

  1. 👍 0
  2. 👎 0
  3. 👁 118
asked by Lost
  1. you have three equations and three unknowns
    ... the unknowns are ... a, Vo, and So

    144 = 1/2 a (.5^2) + Vo .5 + So

    152 = 1/2 a (1^2) + Vo 1 + So

    128 = 1/2 a (2.5^2) + Vo 2.5 + So

    solve the system for a, Vo, and So
    ... use the resulting equation to find max height and flight time
    ... max height occurs at max time (on the axis of symmetry ... -b/2a)
    ... flight time is when s equals zero

    1. 👍 0
    2. 👎 0
    posted by R_scott

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    during a scienceday learners use a plastic cold drink bottle as a rocket. they use a bicycle pump to increase the bottle. when the pressure becomes high enough, the bottle is launched vertically upward into the air. the bottle

    asked by warren on March 24, 2015
  2. Math

    A bottle rocket travels along a parabolic path and reaches a maximum height of 21 feet after traveling a horizontal distance of 7 feet. A) Write a quadratic function of the form y=a(x-h)^2 +k that models the bottle rocket's path,

    asked by Jamie on December 7, 2014
  3. physics

    During a Science day learners use a plastic cold drink bottle as a rocket.They use a bicycle pump to increas the presure inside the bottle.When the presure becomes high enough,the bottle is launched vertically upwards into the

    asked by Thabang on January 22, 2012
  4. physics

    The engine of a toy rocket supplies an average acceleration of 38.0 m/s/s to the rocket for an interval of 0.80 s. A.)If the toy roocket is launched vertically, how high does it rise in this interval? B.) How fast is the rocket

    asked by Kendra on January 19, 2010
  5. physics

    A stationary rocket is launched vertically upward. After 4s, the rocket's fuel is used up and it is 225.6 m above the ground. At this instant the velocity of the rocket is 112,8 m/s. Then the rocket undergoes free fall. Ignore the

    asked by clement on March 8, 2014
  6. science

    A rocket launched accelerates at 3.5m/s^2 in 5.90 secs and2.98m/s^2 in the next 5.98 secs and then experiences a free fall. What time will the rocket be in air? Assume that the rocket is launched from the ground.

    asked by Anonymous on September 2, 2013
  7. science

    3.A rocket launched accelerates at 3.5m/s^2 in 5.90 secs and2.98m/s^2 in the next 5.98 secs and then experiences a free fall. What time will the rocket be in air? Assume that the rocket is launched from the ground.

    asked by mano on July 6, 2016
  8. Physics

    A toy rocket is launched upwards from rest. The rocket engine will cause the rocket to accelerate at 25 m/s^2 for 3.0 seconds. a) How fast is the rocket moving aft the end of the 3 seconds? b) What is the maximum height reached by

    asked by Sam on October 7, 2010
  9. chemistry

    I was asked to bring something into class with a pressure less than 1.0 atm, after researching i found out that if I heated a bottle it will shrink and therefore this bottle will have the needed pressure. the problem is that after

    asked by claudia on February 6, 2007
  10. Math/calculus

    a toy rocket is shot into the air at the top of a building so that its height above the ground t seconds after the rocket is launched is given by the formula h(t)= -3t cubed + 6t squared + 27t feet from liftoff until the rocket

    asked by lola on July 13, 2012

More Similar Questions