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Ben and Josh went to the roof of their 40-foot tall high school to throw their math books off the edge.
The initial velocity of Ben’s book was 60 feet per second while the initial velocity of Josh’s book was 48
feet per second. The equation ℎ (t) = −16t( + vt + s can be used to represent the situation where ℎ
is the height of the textbook at time t seconds, v is the initial upward velocity, and s is the starting point.
Whose textbook reaches the ground first and by how many seconds

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sqdancefan

Answer:

  • Josh's book lands first
  • Ben's lands about 0.648 seconds later

Step-by-step explanation:

Using the given equation for v=60 and s=40, the height of Ben's book is ...

  h(t) = -16t² +60t +40

We want to find t when h(t) = 0, so we're looking for the solution to ....

  0 = -16t² +60t +40

Using the quadratic formula, we find the positive value of t to be ...

  t = (-60 -√(60² -4(-16)(40)))/(2(-16)) = (15 +√385)/8 ≈ 4.3277

__

Similarly, the height of Josh's book is ...

  0 = -16t² +48t +40

  t = (-48 -√(48² -4(-16)(40)))/(2(-16)) = (12 +√304)/8 ≈ 3.6794

__

The time before Josh's book lands is shorter by ...

  4.3277 -3.6794 ≈ 0.6482 . . . . . seconds

Josh's book reaches the ground first, by about 0.648 seconds.

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