(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In 1939, Joe Sprinz of the San Francisco Seals Baseball Club attempted to catch a ball dropped from a blimp at a height of 800 ft (for the purpose of setting a record).

(a) How long does it take for a ball to drop 800 ft?

(b) What is the velocity of a ball in miles per hour after an 800-ft drop? (88 ft/s = 60 mi/h)

Note: Wind resistance cannot be ignored in this problem. However, even with the slowing effect of wind resistance, the impact of the ball slammed Sprinz's glove hand into his face, fractured his upper jaw in 12 places, broke 5 teeth, and knocked him unconscious. Of course, he dropped the ball.

2. Relevant equations

h(t) = -1/2g(t)^2 + V(t) + S

3. The attempt at a solution

(a) I am pretty confident I solved this portion correctly. I took the formula h(t) = -1/2g(t)^2 + V(t) + S and plugged in the information I was given:

1. Solved for t: 0 = (-1/2)(32)(t)^2 + (0)(t) + 800

2. 0 = -16(t)^2 + 800

3. 16(t)^2 = 800

4. t^2 = 50

5. t = 7.07 seconds.

(b) Now I have to solve for V, correct? I came up with 154.25 mi/h using the following steps:

1. Take the derivative of the given formula: h(t) = -g(t) + V

2. Plug in the values given: h(7.07) = -32(7.07) + V

3. I set h=0 here to solve for V: 0 = -226.24 + V, or V = 226.24 ft/s

4. Converted to mi/h: 226.24 ft/s * (60 mi/h / 88 ft/s) = 154.25 mi/h.

I am just a little unsure about (b). Can anyone else verify it and let me know if I made any mistakes or not?

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# Homework Help: Calculus I - Velocity/Distance/Time

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