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Math Help - Projectile Motion - Vector

  1. #1
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    Projectile Motion - Vector

    The velocity of a particle moving in the xy plane is given by = (5.2 t - 4.8 t2) + 8.0, with in meters per second and t (> 0) in seconds. (a) What is the acceleration when t = 2.3 s? (b) When (if ever) is the acceleration zero? (c) When (if ever) does the speed equal 10 m/s?

    I am able to solve for (a) and (b), but (c) gives me complex numbers as a result of the quadratic equation.

    Would the answer for (c) be never?

    Thanks!
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  2. #2
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    Hello silencecloak
    Quote Originally Posted by silencecloak View Post
    The velocity of a particle moving in the xy plane is given by = (5.2 t - 4.8 t2) + 8.0, with in meters per second and t (> 0) in seconds. (a) What is the acceleration when t = 2.3 s? (b) When (if ever) is the acceleration zero? (c) When (if ever) does the speed equal 10 m/s?

    I am able to solve for (a) and (b), but (c) gives me complex numbers as a result of the quadratic equation.

    Would the answer for (c) be never?

    Thanks!
    I suspect you forgot the \pm sign in part (c).

    Speed = \sqrt{(5.2t-4.8t^2)^2+64}=10

    \Rightarrow (5.2t-4.8t^2)^2=36

    \Rightarrow 5.2t-4.8t^2=\color{red}\pm\color{black}6

    Taking the - sign gives a real, positive root, which (if my arithmetic is correct) is t = 1.78

    Grandad
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