Question

29. BASKETBALL When Jerald shoots a free throw, the ball is 6 feet from the floor and has

Answer 1

Answer:

  a) j(t) = -16t^2 +20t +6

  b) 1 second

  c) less time

Step-by-step explanation:

The general equation for vertical motion is ...

  $h(t)=-\dfrac{1}{2}gt^2+v_0t+h_0\\\text{where v_0 is the initial upward velocity, and h_0 is the initial height}$

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a) j(t) = -16t^2 +20t +6 . . . . . filling in the given initial values, with g=32 ft/s^2

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b) We want to find the larger of the solutions to ...

  j(t) = 10 = -16t^2 +20t +6

Subtracting 6 and dividing by -4, we have ...

  -1 = 4t^2 -5t

  4t^2 -5t +1 = 0 . . . . add 1, put in standard form

  (4t -1)(t -1) = 0 . . . . . factor

  t = 1/4 or 1

The ball is in the air 1 second before reaching the hoop.

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c) In generic terms, the equation of motion for a given shooting height at the same upward velocity will be ...

  10 = -16t^2 +20t + h0

  -16t^2 +20t +(h0 -10) = 0

Using the quadratic formula, we find the larger solution to be ...

  t = (-(20) -√(20² -4(-16)(h0 -10)))/(2(-16))

  t = (5/8) + √(64h0 -240)/32 = (5 +√(4h0 -15))/8

This value increases as h0 increases, so the ball will be in the air less time when Raymond shoots.