The parametric equations for the path of a projectile launched at a height feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is
Given by The center field fence in a ballpark is feet
High and feet from home plate.The ball is hit 3 feet above the ground.It leaves the bat at an angle
Of degrees with the horizontal at a speed of 100 miles per hour as shown in the figure.Find the
Minimum angle at which the ball must leave the bat in order for the hit to be a home run using the
Parametric equations Round your answer to one
Decimal place.

Question

The parametric equations for the path of a projectile launched at a height  feet above the ground, at an angle  with the horizontal and having an initial velocity of  feet per second is
Given by  The center field fence in a ballpark is  feet
High and  feet from home plate.The ball is hit 3 feet above the ground.It leaves the bat at an angle
Of  degrees with the horizontal at a speed of 100 miles per hour as shown in the figure.Find the
Minimum angle at which the ball must leave the bat in order for the hit to be a home run using the
Parametric equations  Round your answer to one
Decimal place.

Quizplus · Accepted Answer

To hit a home run, the ball must travel a horizontal distance of 11ebbd4d_3efa_3add_8a0a_43d8e22b8411_TB8202_11 feet (the distance from home plate to the fence) and reach a vertical height of 11ebbd4d_3efa_3ade_8a0a_8776b4f4d4c6_TB8202_11 + 11ebbd4d_3efa_3adf_8a0a_6310cb28e7ed_TB8202_11 = 22 feet (the height of the fence plus the initial height of the ball).

Using the given parametric equations, we can solve for when the ball reaches a height of 22 feet:

11ebbd4d_3efa_3ae0_8a0a_c43a3aab3de3_TB8202_11 
11ebbd4d_3efa_3ae0_8a0a_c43a3aab3de3_TB8202_11

Now we can solve for t:

11ebbd4d_3efa_3ae1_8a0a_38ecadede9f8_TB8202_11

Substituting this value of t into the x-equation, we can find the horizontal distance the ball traveled:

11ebbd4d_3efa_3ae2_8a0a_8e2c75b721aa_TB8202_11

So the ball must travel a horizontal distance of 11ebbd4d_3efa_3ae3_8a0a_297e0dad86be_TB8202_11 feet.

Therefore, to hit a home run, the ball must leave the bat at an angle such that it can travel a horizontal distance of 11ebbd4d_3efa_3ae4_8a0a_297e0dad86be_TB8202_11 feet in the air. The minimum angle can be found using the range equation:

11ebbd4d_3efa_3ae5_8a0a_d97fee8f0407_TB8202_11

Solving for θ, we get:

11ebbd4d_3efa_3ae6_8a0a_c658bcbea1c4_TB8202_11

Rounding to one decimal place, the answer is B: 38.9 degrees.

The Parametric Equations for the Path of a Projectile Launched