Question

please show worked problem;

The range R of a projectile fired from the origin over horizontal ground is the distance from the origin to the point of impact. If the projectile is fired with an initial velocity v0 at an angle a with the horizontal, then the range is given by the formula below, where g is the downward acceleration due to gravity. Find the angle a for which the range R is the largest possible. R = v^2/g sin 2alpha alpha = degree (Use angle measures greater than or equal to 0 and less than or equal to 90.)

Answer 1

You want an angle that gives you the biggest possible value of "sin(2θ)".

So, first question: What is the biggest possible value that "sin(something)" can have? (Hint: "1". The sine of an angle is always somewhere between −1 and +1, so the max possible value is "1").

Next question: What angle "x" to you have to plug in, to make "sin(x)" have its maximum value? (i.e. what angle has the greatest sin?)

Once you've found "x", set that equal to "2θ":
x = 2θ
90 = 2θ
θ = 45 degrees