Question

5. During the eruption of Mount St. Helens in 1980. debris was ejected at a speed of over 440 feet per second

Answer 1

Answer:

  3500 ft

Step-by-step explanation:

We assume you intend the equations to be ...

$y(t)=-16t^2+425t+8200\\x(t)=113t$

Then we can solve the second equation for t and use that in the first equation. We can solve the first equation for y=6000.

  x = 113t

  t = x/113

  y(t) = y(x/113) = -16(x/113)² +425(x/113) +8200 = 6000

  (16/12769)x² -(425/113)x -2200 = 0 . . . . . . subtract 6000, multiply by -1

Using the quadratic formula, the positive solution is ...

  x = ((425/113) +√((-425/113)² -4(16/12769)(-2200))/(2(16/12769))

The fraction in the denominator can be inverted and used as a multiplier. We also use a√b = √(a²b) to simplify the radical.

  x = (48025 +√4104275825)/32

  x ≈ 3502.8

Rock was thrown about 3500 feet horizontally.