Parabolic 79764

In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court?

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a_x^2+b_x+c=y \\ A=(-5,0.80) \\ V=(0,1.5) \\ k=23.77\text{m} \\ a=-1 \\ -A_x^2+b\cdot A_x+c=A_y \\ -V_x^2+b\cdot V_x+c=V_y \\ -(-5{)}^2+b\cdot (-5)+c=0.80 \\ -0^2+b\cdot 0+c=1.5 \\ 5b-c=-25.8 \\ c=1.5 \\ c=\frac{1.5}{1}=1.5 \\ b=\frac{-25.8+c}{5}=\frac{-25.8+1.5}{5}=-4.86 \\ b=\frac{-243}{50}=-4.86 \\ c=\frac{3}{2}=1.5 \\ {B}_x=k/2=23.77/2=\frac{2377}{200}=11\frac{177}{200}=11.885\text{m} \\ {B}_y=-B_x^2+b\cdot B_x+c=-11.885^2+(-4.86)\cdot 11.885+1.5\doteq -197.5143 \\ x=0 \end{gathered}$$

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