Question

Craig shoots a basketball at an angle of 55" from the horizontal. It leaves his hands 6 feet from the ground with a velocity of 21 ft/s.Step 2 of 2: Determine the height of the ball when it is 2 feet away horizontally. Round to the nearest tenth.AnswerHow to enter your answer (opens in new window)okay

Answer 1

8.422 ft

Step 1

given:

$\begin{gathered} x=12t \\ y=-16t^2+17.2t+6 \end{gathered}$

hence

a)find the time wich the distance horizontally is 2 ft

so

let

$x=2$

now ,replace and solve for t

$\begin{gathered} x=12t \\ 2=12t \\ divide\text{ both sides by 12} \\ \frac{2}{12}=\frac{12t}{12} \\ \frac{1}{6}=t \\ t=\frac{1}{6}\text{ seconds} \end{gathered}$

b)now, find the heigth for the given time

let

$t=\text{ }\frac{1}{6}\text{ sec}$

now, replace in the parametric equation

$\begin{gathered} y=-16t^2+17.2t+6 \\ y=-16(\frac{1}{6})^2+17.2(\frac{1}{6})+6 \\ y=-\frac{16}{36}+\frac{17.2}{6}+6 \\ y=-0.4444+2.8666+6 \\ y=8.422 \end{gathered}$

therefore, the answer is

8.422 ft

I hope this helps you