Don asked in Science & MathematicsMathematics · 1 decade ago

calculus problem .....?

Applications of Integrals : Velocity and Acceleration

Newton discovered that the falling acceleration of all objects in a vacuum, regardless of their sizes and weights, is the same. A raindrop falls down to earth with the same acceleration as a big metal ball drops from the edge of a building. He came up with the value of 9.8 meters per square second (s2) for the falling acceleration of all objects.

Thus, knowing that the acceleration of an object is the derivative of its velocity, we can conclude that for any object with velocity of v(t), where t is the time for covering the distance,

V '(t) = -9.8 m/s2

1. Using this equation, find the function of the velocity of a raindrop. If you are using integration, how will you determine the value of the constant C in the integral function?

2. A raindrop at rest, in a cloud 7600 meters above earth, starts its journey toward earth. Determine how long it takes the raindrop to reach the ground.

3. Determine its velocity when it reaches the ground.

4. The velocity of a bullet fired from a pistol is about 200 meters per second, which could cause serious injury or even death. Compare the velocity of a raindrop to this velocity. Explain why the raindrop, which has a far greater velocity than a bullet, does not harm us.

keywords: integration, integrates, integrals, integrating, double, triple, multiple

2 Answers

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  • cidyah
    Lv 7
    1 decade ago
    Favorite Answer

    2)

    -4.9t^2+1700=0

    solve for t

    -4.9 t^2 = -1700

    t^2 = 346.9388

    t=18.63 seconds

    3)

    velocity = -9.8 t

    -9.8(18.63) =-182.57 meters/sec

  • boase
    Lv 4
    4 years ago

    f (x) = x^3 - 12x + a million . . . the 1st spinoff set to 0 unearths turning or table certain factors f ' (x) = 3x^2 - 12 3x^2 - 12 = 0 3 * (x + 2) * (x - 2) = 0 x = 2 ... x = - 2 . . . the 2d spinoff evaluated at x = 2 and -2 determines if those factors are min, max, or neither. f ' ' (x) = 6x f ' ' (2) = 6*2 = 12 <== valuable cost shows x=2 is a close by minimum f ' ' (-2) = 6*(-2) = -12 <== unfavorable cost shows x=-2 is a close by optimum a.) x = - 2 is a optimum, and x=2 is a minimum ... so x = - infinity to -2 is increasing x = -2 to +2 is reducing x = +2 to + infinity is increasing b.) f (-2) = (-2)^3 - 12*(-2) + a million = 17 f (2) = (2)^3 - 12*(2) + a million = - 15 c.) . . . the 2d spinoff set to 0 unearths inflection factors, or the place concavity differences 6x = 0 x = 0 <=== inflection element x = - 2 is a optimum, so could desire to be concave down concavity differences on the inflection element(s) ... so x = - infinity to 0 is concave down x = 0 to + infinity is concave up

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