pre-calc

posted by .

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 by h(x)= -0.0128x^2+x+200 where x is the horizontal distance of the projectile from the base of the cliff.

a) how far from the base of the cliff is the height of the projectile at its maximum?
b) find the maximum height of the projectile.
c) how far from the base of the cliff will the projectile strike the water?
d) when the height of the projectile is 100 feet above the water, how far is it horizontally from the cliff?

  • pre-calc -

    This is just a good old parabola.

    max height occurs at x=-b/2a = -1/-.0256 = 39.0625

    h(39.0625) = 219.531

    h(x) = 0 at x = 170 approx.

    h(x) = 100 at x = 135.7

  • pre-calc -

    thanks! i posted some other questions that i really need help with too

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    A projectile is fired directly upward with a muzzle velocity of 860 feet per second from a height of 7 feet above the ground. a. Determine a function for the height of the projectile t seconds after it’s released. b. How long does …
  2. math

    If a projectile is launched from a platform 30 feet high with an initial velocity of 128 feet per second, then the height of the projectile at t seconds is given by s(t) = –16t2 + 128t + 30 feet. (a) At what time does the projectile …
  3. Math

    A projectile is fired straight up from a cliff which is 200 feet above ground with an initial velocity of 220 ft/sec. Assume that the only force affecting the projectile during flight is from gravity which produces a downward acceleration …
  4. Physics

    A projectile is fired straight up from a cliff which is 200 feet above ground with an initial velocity of 220 ft/sec. Assume that the only force affecting the projectile during flight is from gravity which produces a downward acceleration …
  5. Dynamics

    A French artillerist, Captain A. Le Duc, developed an empirical formula for the velocity of a projectile in terms of the distance traveled by the projectile in the bore. For a 155-mm gun this equation is v = 3309s /(70 + s) where s …
  6. College Algebra

    Show all work. A projectile is fired from a cliff 100 ft above the water at an inclination of 45 degrees to the horizontal, with a muzzle velocity of 260 ft/second. The height of the projectile above the water is given by h(x)= ((-32x^2)/(260)^2)+x+100, …
  7. Trig

    The path of a projectile fired at an inclination t0 to the horizontal with initial velocity v feet per second is a parabola. The horizontal distance R, in feet, that the projectile travels is given by R = v2sin(2t)/32.2. What is R …
  8. calculus

    The height of a projectile launched into the air is given by h (t)= -16t^2 + 48t + 60, where h is the height of the projectile in feet above the ground and t is the number of seconds after its launch. Find the *instantaneous rate of …
  9. 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 being …
  10. Algebra

    The function H(t) = -16t2 + vt + s shows the height H (t), in feet, of a projectile launched vertically from s feet above the ground after t seconds. The initial speed of the projectile is v feet per second. Part A: The projectile …

More Similar Questions