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:

Neurotransmitters

Chemicals that transmit signals across a synapse from one neuron to another in the brain and nervous system.

Autoreceptors

Specialized receptor molecules located on a neuron that respond to the neurotransmitter released by that neuron, regulating its own function.

Presynaptic Side

The part of a synapse that releases neurotransmitters from the axon terminal of a neuron into the synaptic cleft, initiating a neural signal.

Neurotransmitters

Chemical messengers released by neurons that transmit signals across a chemical synapse, such as between neurons or from neurons to muscles.