Vertically 65984

We threw the stone vertically upwards at a speed of v = 15 m/s. How long will it be at a) 10 m, b) 12 m?

Correct answer:

t₁ = 0.982 s
t₂ = 2.0761 s
t₃ = s NA

v_{0} = 15 m/s h_{1} = 10 m g = 9.81 m/s^{2} h = v_{0} \cdot t - \frac{1}{2} \cdot g \cdot t^{2} h_{1} = v_{0} \cdot x - 0.5 \cdot g \cdot x^{2} 10 = 15 \cdot x - 0.5 \cdot 9.81 \cdot x^{2} 4.905 x^{2} - 15 x + 10 = 0 a = 4.905; b = - 15; c = 10 D = b^{2} - 4 a c = 1 5^{2} - 4 \cdot 4.905 \cdot 10 = 28.8 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 5 \pm 2 8 . 8}{9 . 8 1} x_{1, 2} = 1.529052 \pm 0.54705 x_{1} = 2.076102257 x_{2} = 0.982001718 t_{1} = x_{2} = 0.982 = 0.982 s

t_{2} = x_{1} = 2.0761 = 2.0761 s

h_{2} = 12 m h_{2} = v_{0} \cdot y - 0.5 \cdot g \cdot y^{2} 12 = 15 \cdot y - 0.5 \cdot 9.81 \cdot y^{2} 4.905 y^{2} - 15 y + 12 = 0 a = 4.905; b = - 15; c = 12 D = b^{2} - 4 a c = 1 5^{2} - 4 \cdot 4.905 \cdot 12 = - 10.44 D < 0 y_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 5 \pm - 1 0 . 4 4}{9 . 8 1} y_{1, 2} = \frac{1 5 \pm i 1 0 . 4 4}{9 . 8 1} y_{1, 2} = 1.529052 \pm 0.329368 i y_{1} = 1.529052 + 0.3293678781122 i y_{2} = 1.529052 - 0.3293678781122 i t_{3} = N A

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