The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 25.5 m/s is h

Question

The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 25.5 m/s is h = 2 + 25.5t ? 4.9t2 after t seconds. (Round your answers to two decimal places.) (a) Find the velocity after 2 s and after 4 s. v(2) = 5.9 Correct: Your answer is correct. m/s v(4) = -13.7 Correct: Your answer is correct. m/s (b) When does the projectile reach its maximum height? 2.60 Correct: Your answer is correct. s (c) What is the maximum height? 37.2 Incorrect: Your answer is incorrect. m (d) When does it hit the ground? 5.36 Incorrect: Your answer is incorrect. s (e) With what velocity does it hit the ground? 27.03 Incorrect: Your answer is incorrect. m/s

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Dulcie 4 years 2021-07-27T18:18:28+00:00 1 Answers 144 views 0

Answers ( )

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    2021-07-27T18:19:54+00:00

    Answer:

    a) v(2\,s) = 5.9\,\frac{m}{s}, v(4\,s) = -13.7\,\frac{m}{s}, b) t = 2.602\,s, c) h(2.602\,s) = 35.176\,m, d) t = 5.281\,s, e) v(2.602\,s) = -26.254\,\frac{m}{s}

    Explanation:

    a) The velocity function is determined by deriving the position function in time:

    v(t) = 25.5-9.8\cdot t

    Velocities after 2 seconds and 4 seconds are, respectively:

    v(2\,s) = 5.9\,\frac{m}{s}

    v(4\,s) = -13.7\,\frac{m}{s}

    b) The maximum height is reached when velocity is equal to zero:

    25.5-9.8\cdot t = 0

    The time when the projectile reaches the maximum height:

    t = 2.602\,s

    c) The maximum height is:

    h (2.602\,s) = 2 + 25.5\cdot (2.602\,s)-4.9\cdot (2.602\,s)^{2}

    h(2.602\,s) = 35.176\,m

    d) The projectile hits the ground when height is equal to zero:

    -4.9\cdot t^{2}+25.5\cdot t + 2 =0

    The roots of the second order polynomial are presented below:

    t_{1} \approx 5.281\,s

    t_{2} \approx -0.077\,s

    The first one is the only reasonable solution in physical terms.

    t = 5.281\,s

    e) The velocity of the projectile when it hits the ground is:

    v(2.602\,s) = 25.5-9.8\cdot (5.281\,s)

    v(2.602\,s) = -26.254\,\frac{m}{s}

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )