Write the Word or Phrase That Best Completes Each Statement $$\mathrm { R } = \frac { \mathrm { v } _ { 0 } ^ { 2 } } { \mathrm {~g} } \sin ( 2 \theta )$$

question 218

Short Answer

Write the word or phrase that best completes each statement or answers the question.
-The path of a projectile fired at an inclination θ (in degrees) to the horizontal with an initial velocity v0 is a
parabola. The range R of the projectile, that is, the horizontal distance that the projectile travels, is found by using the
formula $$\mathrm { R } = \frac { \mathrm { v } _ { 0 } ^ { 2 } } { \mathrm {~g} } \sin ( 2 \theta )$$ s where $g$ is the acceleration due to gravity. Suppose the projectile is fired with an initial velocity of 400 feet per se and $g = 32$ feet per second 2 . What angle $\theta , 0 ^ { \circ } \leq \theta < 90 ^ { \circ }$ , would you select for the range to be 2500 feet? (There should be two values of $\theta . )$

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Definitions:

Antifreeze

A liquid added to the water in a cooling system to lower its freezing point, commonly used in automobile engines.

Cooling System

A system designed to remove heat from an area or machinery, commonly using a fluid or air to transfer heat away.

Algebraic Expression

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operation symbols, but no equality sign.

Ratio

A relationship between two numbers indicating how many times the first number contains the second.