A projectile is fired with an initial speed of 75.2 m/s at an angle od 34.5 degrees above the horizontal on a long flat firing range. Determine (a) th

Every time a projectile is fired with some velocity V atsome angle, you must break up the velocity into its x and ycomponents since velocity is a vector. The x component of thevelocity is ${\displaystyle Vx=V\cos (?)}$, and the y component is ${\displaystyle Vy=V\sin (?)}$. Now, in these range problems there are generally only twoequations that you will use. One equation will be for thex-component and the other will be for the y-component. Theseequations are ${\displaystyle X=Vx\times T}$, (X=distance traveled in the x direection,T=total time), and ${\displaystyle Y=Y\oplus VyT+\left(\frac{1}{2}\right)aT2}$.
Everytime you havethese equations two things happen. In the x-direction, the velocityVx is always constant since there are no forces acting in thisdirection. In the y-direction however, there is a force, gravity,which tends to act down towards the ground. Since we take anymotion moving up in the y-direction to be positive, gravity pointsdown and should be negative. So the equation in the y should be ${\displaystyle Y=Y\oplus VyT-\left(\frac{1}{2}\right)gT2}$
, where g is gravity. Now you are readyto solve the problem. We will answer b first. Since the projectileis fired on a long flat range, Yo=0 since there is no initial hillwith height Yo. Since at T=0 the object is on the ground gettingready to be fired and at T=? after being fired it lands again(Y=0), set ${\displaystyle 0=VyT-\left(\frac{1}{2}\right)g{T}^2}$ and solve for T, this is the total timein air. Now for part a, since the trajectory of the ballis symetrical, at exactly 1/2 the total time the ball will be atits maximum height. So cut the time you got for part b i half andplug it into the equation ${\displaystyle Y=VyT-\left(\frac{1}{2}\right)g{T}^2}$. For part c, thetotal distance covered deals with the X direction and so youshould take the total time of flight and plug that into theequation X=VxT. For part d, its a bit ridiculous and I willpost a picture of the solution of it after thispost.