Math

A ball is kicked into the air and follows a path described by h(t)=-4.9t^2 +8.4t+0.6, where t is the time in seconds and h is the height of the balls in metres. Determine the maximum height of the ball, to the nearest tenth of a metre.

  1. 👍 0
  2. 👎 0
  3. 👁 123
asked by Trisha
  1. This is a parabola, and the peak will be halfway between the roots.
    so the roots are...
    0=4.9t^2 -8.4t-0.6
    0 =t^2 -1.71t-0.122
    t=(1.71/2 +- sqrt....

    so the midpoint, or the max height occures at t=1.71/2=.86 seconds.
    then height is h(t)=-4.9t^2 +8.4t+0.6 with t=above.

    If you are in calculus, it is much easier, find when it stop rising upward.
    dh/dt=0=-9.8t+8.4, solve for t..then solve for h(that t).














    1.71+-sqrt(2.92-.488)/2
    t= -.86 +-.78
    halfway between these roots are -.86, so the beak occurs

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A football is kicked from the ground at 27 m/s at an angle of 42 degrees above the horizontal (ground). No one gets in the way until after it hits the ground. Use the value g=9.8 m/s^2. Assuming that the ground is level and that

    asked by Sandy on October 27, 2010
  2. Physics

    A football is kicked from the ground at 27 m/s at an angle of 42 degrees above the horizontal (ground). No one gets in the way until after it hits the ground. Use the value g=9.8 m/s^2. Assuming that the ground is level and that

    asked by Sandy on October 27, 2010
  3. Math( please help)

    a ball is kicked in the air from the top of a cliff. the path the ball travels is given by the equation h(t)=-5t^2+17t+22 where h(t) is the height in metres and t is the time in seconds a) what is the maximum height that the ball

    asked by Julie on October 16, 2011
  4. Math( please help)

    a ball is kicked in the air from the top of a cliff. the path the ball travels is given by the equation h(t)=-5t^2+17t+22 where h(t) is the height in metres and t is the time in seconds a) what is the maximum height that the ball

    asked by Julie on October 16, 2011
  5. Science :)

    A football is kicked from the ground at 27 m/s at an angle of 42 degrees above the horizontal (ground). No one gets in the way until after it hits the ground. Use the value g=9.8 m/s^2. Assuming that the ground is level and that

    asked by Sandy on October 28, 2010
  6. physics - help!

    A soccer ball is kicked with a speed of 22m/s at an angle of 35.0º above the horizontal. Can someone show me how to find how long the ball was in the air if the ball lands at the same level from which it was kicked?

    asked by Mariam on April 10, 2018
  7. Physics

    A soccer ball kicked on a level field has an initial vertical velocity component of 15 meters per second. Assuming the ball lands at the same height from which it was kicked, what is the total time the ball is in the air? [Neglect

    asked by Shannon on November 14, 2012
  8. Physics

    Emmy kicks a soccer ball up at an angle of 45° over a level field. She watches the ball\'s trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. Assume that air resistance is

    asked by Breauna on February 13, 2015
  9. Physics Projectile Motion

    A ball is kicked with an initial velocity of 21 m/s in the horizontal direction and 16 m/s in the vertical direction. (Assume the ball is kicked from the ground.) (a) At what speed does the ball hit the ground? (b) For how long

    asked by Abby on September 29, 2015
  10. Physics Kinematics.

    A ball is kicked with an initial velocity of 21 m/s in the horizontal direction and 16 m/s in the vertical direction. (Assume the ball is kicked from the ground.) (a) At what speed does the ball hit the ground? (b) For how long

    asked by Destiny on September 28, 2015

More Similar Questions