The Parametric Equations for the Path of a Projectile Launched $\theta$

question 39

Multiple Choice

The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle $\theta$ with the horizontal and having an initial velocity of $v _ { 0 }$ feet per second is given by $x = \left( v _ { 0 } \cos \theta \right) t$ and $y = h + \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 }$ . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of $\theta$ degrees with the horizontal at a speed of 100 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball.

• A)\(x = \left( \frac { 440 } { 3 } \cos \theta \right) t , y = 2 + \left( \frac { 440 } { 3 } \sin \theta \right) t\)
• B) \(x = 2 + \left( \frac { 440 } { 3 } \sin \theta \right) t , y = \left( \frac { 440 } { 3 } \cos \theta \right) t\)
• C)\(x = 2 + \left( \frac { 440 } { 3 } \sin \theta \right) t - 16 t ^ { 2 } , y = \left( \frac { 440 } { 3 } \cos \theta \right) t\)
• D) \(x = \left( \frac { 440 } { 3 } \sin \theta \right) t , y = 2 + \left( \frac { 440 } { 3 } \cos \theta \right) t - 16 t ^ { 2 }\)
• E)\(x = \left( \frac { 440 } { 3 } \cos \theta \right) t , y = 2 + \left( \frac { 440 } { 3 } \sin \theta \right) t - 16 t ^ { 2 }\)

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Definitions:

NPV

A financial metric that calculates the total value of a project or investment by discounting future cash flows back to their present value and subtracting initial investment cost.

Scenario Analysis

A business planning technique in which the implications of variations in planning assumptions are explored. Also known as “what-if-ing.”

Abandonment Option

A financial decision allowing companies to cease a project or investment to avoid further losses.

NPV

Net Present Value; a calculation used to assess the profitability of an investment, considering the present value of its cash flows.