Solve the Problem $\theta \text { (in degrees) }$ To the Horizontal with an Initial Velocity

question 369

Short Answer

Solve the problem.
-The path of a projectile fired at an inclination $\theta \text { (in degrees) }$ to the horizontal with an initial velocity $\mathrm { v } _ { 0 }$ is a
parabola. The range R of the projectile, that is, the horizontal distance that the projectile travels, is found by using the
formula $$\mathrm { R } = \frac { \mathrm { v } _ { 0 } ^ { 2 } } { \mathrm {~g} } \sin ( 2 \theta )$$ where g is the acceleration due to gravity. Suppose the projectile is fired with an initial velocity of 400 feet per seconds
and g = 32 feet per $\operatorname { second } \mathrm { d } ^ { 2 }$ . 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:

Exercise Price

The price at which an option holder can buy or sell the underlying asset.

Money Spread

The difference between two prices or rates, often used to describe the gap between bid and ask prices in financial markets.

Call Option

A financial contract that gives the holder the right, but not the obligation, to buy a stock, bond, commodity, or other assets at a predetermined price within a set time frame.

Covered Call

An options strategy where an investor holds a long position in an asset and sells call options on that same asset to generate income from the option premiums.