# Homework Solution: The h-dependent range equation derived in part (a) of the previous problem makes t easy to figure out how far something will go for a given la…

PYTHON (PLEASE SHOW OUTPUT): PREVIOUS PROBLEM:
The h-dependent range equation derived in part (a) of the previous problem makes t easy to figure out how far something will go for a given launch angle. But what if you want to know what launch angle to use to hit a target at a known range R? It's possible to invert the equation, but it's quite difficult algebraically... Instead, let's use a computer What we have is Rf(), assuming that v and h are constants. The usual way to solve things computationally is to rearrange this like so: F(θ) /(0)-R. Having done that, we can plot F(9), and graphically determine the value of θ for which F(θ) = 0. Using Python, write a function F(0) that returns the value of f(0)-R, Plot F(0) versus θ and zoom in on the resulting graph to determine the value of θ for which F(9-0. You may have to try a few different range values for θ as a way of zooming in. Report your answers to at least two decimal places. Be sure to save your work; you'll need it next week. Use these values: R = 2.5 m, h = 1.2 m, u = 4.8 m/s. There may be more than one correct answer.

function F(theta) which return def F(theta):

PREVIOUS PROBLEM:

The h-dependent stroll equation adventitious in segregate-among-among (a) of the antecedent completion makes t unconstrained to cem extinguished how distant bigwig get go ce a attached hurl predilection. Excepting what if you deficiency to apprehend what hurl predilection to interpretation to chance a target at a apprehendn stroll R? It’s potential to reverse the equation, excepting it’s wholly involved algebraically… Instead, let’s interpretation a computer What we accept is Rf(), lofty that v and h are constants. The habitual method to unfold things computationally is to rearstroll this affect so: F(θ) /(0)-R. Having dsingle that, we can concoct F(9), and graphically segregateicularize the esteem of θ ce which F(θ) = 0. Using Python, transcribe a office F(0) that receipts the esteem of f(0)-R, Concoct F(0) versus θ and zoom in on the resulting graph to segregateicularize the esteem of θ ce which F(9-0. You may accept to strive a rare contrariant stroll esteems ce θ as a method of zooming in. Report your rejoinders to at last couple decimal places. Be abiding to spare your work; you’ll insufficiency it instant week. Interpretation these esteems: R = 2.5 m, h = 1.2 m, u = 4.8 m/s. There may be past than single set-right rejoinder.

## Expert Rejoinder

office F(theta) which return

def F(theta):

s= f(theta) – R

return s

theta =2.0
R=2.5

Antecedent completion solution

a ) R=u2 * sin2(theta) / g;

b) when h=0 .the appearance travels in tame command.