A Projectile Is Launched from Ground Level at an Angle $\theta$

question 18

Multiple Choice

A projectile is launched from ground level at an angle of $\theta$ with the horizontal. The initial velocity is $v _ { 0 }$ feet per second and the path of the projectile is modeled by the parametric equations $x = \left( v _ { 0 } \cos \theta \right) t$ and $y = \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 } .$
Use a graphing utility to graph the paths of a projectile launched from ground level with the values given for $\theta$ and $v _ { 0 }$ . Use the graph to approximate the maximum height and range of the projectile to the nearest foot.
$$\theta = 50 ^ { \circ } , \quad v _ { 0 } = 104 \text { feet per second }$$

• A) maximum height \(\approx 12\) feet range \(\approx 171\) feet
• B) maximum height \(\approx 171\) feet range \(\approx 12\) feet
• C) maximum height \(\approx 99\) feet range \(\approx 333\) feet
• D) maximum height \(\approx 333\) feet \(\quad\) range \(\approx 99\) feet
• E) maximum height \(\approx 38\) feet range \(\approx 8\) feet

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Definitions:

Downward-sloping Demand

Refers to the economic principle that, all else being equal, as the price of a good or service decreases, the quantity demanded increases.

Inelastic Demand

A condition in market dynamics where the demand for a product does not significantly change with a change in the product's price.

Competitive Price-searcher

An economic term for a seller that sets its product prices based on what competitors are charging, within a competitive market environment.

Product Differentiation

The process of distinguishing a product or service from others in the market to make it more attractive to a particular target market.