Assume the initial position of the projectile is (0, 6m), . Suppose there is a t

Question

Assume the initial position of the projectile is (0, 6m),

.   Suppose there is a target located at (400m, 115m).

Assuming the same initial projectile position and target position given in Problem 3, find the initial velocity and launch angle required so that the time to impact the target is exactly 15 seconds.  Include results and MATLAB commands.  Verify solution with a plot.

y = -1/2 . gt2 + v0sin(theta)t + y0 x = v0cos(theta)t + x0| g = 9.81 m/s2 Assume the initial position of the projectile is (0, 6m), Suppose there is a target located at (400m, 115m). Assuming the same initial projectile position and target position given in Problem 3, find the initial velocity and launch angle required so that the time to impact the target is exactly 15 seconds. Include results and MATLAB commands. Verify solution with a plot.

Explanation / Answer

clc;

clear all ;

close all;

g=9.81;

y_0=6;

x_0=0;

t_0=15;

%% calculating time

syms V ;

syms x;

V_0=solve(((115-y_0+.5*g*t_0^2)^2+400^2-V^2*t_0^2),V);

%% calcuating projection angles

syms theta;

theta_0=180*solve(400-85.1263*cos(theta)*15,theta)/3.14;

% plotting y vs x for these two projection angles

Y_1=ezplot(-.5*g*(x/(85.1263*cos(71.7806*3.14/180)))^2+x*tan(71.7806*3.14/180)+y_0,[0,400]);

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