Technical Problem 4
Given the following:
If a football is kicked from ground level with an initial velocity v0 at an initial angle of
θ0, then (neglecting drag) after it has traveled a horizontal distance d, it will be at a height
y given by the following
equation:y=d*tan(theta)-0.5g(d*d)/((v0*v0)cos^2(theta)
Suppose a kicker is 50 m from the goal and the goal is 3.4 m high, and that the kicker can
give the ball an initial velocity of 27m/s at any angle up from the horizontal that they
want. If they kick the ball at a very low angle or at a very high angle, it will not make it
over the goal.
Although some kick angles will be too small and some will be too large, there will be a
range of angles for which the kick will make it over the goal. We can figure out what
those angles are by setting d= 50, v0=27, and g = 9.81 and evaluating the equation:y=d*tan(theta)-0.5g(d*d)/((v0*v0)cos^2(theta)
d g for various values of theta (θ) to see which values give
y≥3.4. That is, we’ll find values of theta for which the height of the football is at least
3.4m after it has moved a horizontal distance of 50 m.
Write a program in which the operator enters in the initial velocity and distance from the
goal. The program will then find the minimum and maximum angles that will make this
possible. It will need to start with theta of 1 degree and increment by 1 degree. It is
possible that the operator could enter values that it will be impossible to obtain.
Therefore the program should stop when theta equals 90 degrees without finding an angle
that will get the ball over the goal. The program will need to state that the goal cannot be
reached with those conditions.
For a trial that will work use d=50, v0=27. Theta will be between 26 degrees and 68
degrees. Remember to change theta to radians when using it in the functions.
seems very straight forward to me. we are not here to write the program for you. if you have an actual question about how to do something please post it.