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

Question 113

Short Answer

Solve the problem.
-The path of a projectile fired at an inclination θ (in degrees) \theta \text { (in degrees) } to the horizontal with an initial velocity v0\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 R=v02 gsin(2θ)\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 secondd2\operatorname { second } \mathrm { d } ^ { 2 } . What angle θ,0θ<90\theta , 0 ^ { \circ } \leq \theta < 90 ^ { \circ } would you select for the range to be 2500 feet? (There
should be two values of θ\theta .)

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