Question

Consider a projectile launched at a height h feet above the ground and at an angle $\theta$ with the horizontal. If the initial velocity is $v_0$ feet per second, the path of the projectile is modeled by the parametric equations $x = t(v_0 \cos(\theta))$ and $y = h + (v_0 \sin(\theta))t - 16t^2$. The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit $h = 3$ feet above the ground. It leaves the bat at an angle of $\theta$ degrees with the horizontal at a speed of 107 miles per hour (see figure). (a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and $\theta$. Enter your answers as a comma-separated list of equations.) (b) Use a graphing utility to graph the path of the ball when $\theta = 15^\circ$. Is the hit a home run? $\circ$ Yes $\circ$ No (c) Use a graphing utility to graph the path of the ball when $\theta = 23^\circ$. Is the hit a home run? $\circ$ Yes $\circ$ No (d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.)

          Consider a projectile launched at a height h feet above the ground and at an angle $\theta$ with the horizontal. If the initial velocity is $v_0$ feet per second, the path of the projectile is modeled by the parametric equations $x = t(v_0 \cos(\theta))$ and $y = h + (v_0 \sin(\theta))t - 16t^2$.
The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit $h = 3$ feet above the ground. It leaves the bat at an angle of $\theta$ degrees with the horizontal at a speed of 107 miles per hour (see figure).
(a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and $\theta$. Enter your answers as a comma-separated list of equations.)
(b) Use a graphing utility to graph the path of the ball when $\theta = 15^\circ$. Is the hit a home run?
$\circ$ Yes
$\circ$ No
(c) Use a graphing utility to graph the path of the ball when $\theta = 23^\circ$. Is the hit a home run?
$\circ$ Yes
$\circ$ No
(d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.)

Consider a projectile launched at a height h feet above the ground and at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = t(v0 cos(θ)) and y = h + (v0 sin(θ))t - 16t^2.
The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 3 feet above the ground. It leaves the bat at an angle of θ degrees with the horizontal at a speed of 107 miles per hour (see figure).
(a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and θ. Enter your answers as a comma-separated list of equations.)
(b) Use a graphing utility to graph the path of the ball when θ = 15^∘. Is the hit a home run?
∘ Yes
∘ No
(c) Use a graphing utility to graph the path of the ball when θ = 23^∘. Is the hit a home run?
∘ Yes
∘ No
(d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.)

Added by Tony T.

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