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Area: \( \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{21(21-13)(21-14)(21-15)} \)
\( = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{7056} = 84 \) cm²
#### 84 cm²
A ball is thrown upward with initial velocity 32 m/s from 20 meters high. When does it hit the ground? (Use \( g = 9.8 \, \text{m/s}^2 \))
Equation: \( h(t) = -4.9t^2 + 32t + 20 \)
Set \( h(t) = 0 \): \( -4.9t^2 + 32t + 20 = 0 \)
Use quadratic formula: \( t = \frac{-32 \pm \sqrt{32^2 + 4 \times 4.9 \times 20}}{2 \times 4.9} \)
Discriminant: \( 1024 + 392 = 1416 \), \( \sqrt{1416} \approx 37.65 \)
\( t = \frac{-32 + 37.65}{9.8} \approx 0.68 \) (discard negative root)
More precisely: \( t \approx 6.94 \) seconds