USE MATLAB TO SOLVE:

$4\mathrm{.}12$ The height and speed of a projectile $($such as a thrown ball$)$ launched with a at an angle $A$ to the horizontal are given by:

$h(t)=v_{0}tsin(A)-\frac{1}{2}g{t}^2$

$v(t)=\sqrt[\phantom{2}]{v_0^2-2v_{0}gtsin(A)+g^2{t}^2}$

where $g$ is the acceleration due to gravity. The projectile will strike the ground when $h(t)=0,$ which gives the time to hit $t_{\text{h}\text{i}\text{t}}=2(\frac{v_0}{g})sin(A).$ Suppose that $A=40,v_{-}0=35\frac{m}{s},$ and $g=9\mathrm{.}81\frac{m}{s}2.$ Use the MATLAB relational and logical operators to find the times when

a$.$ The height is no less than $18m.$

b$.$ The height is no less than $10m,$ and the speed is simultaneously no greater than $30\frac{m}{s}.$

Approach

Initialize all of the variables given and then create a plot that shows both speed and height versus time. This will provide a visual aid for confirming the calculations performed below. Remember that the $sin(x)$ command assumes that the input is in radians and this problem has given the angle in degrees.