The horizontal range, R, is modeled by this formula:
R(x)=(v^2*sin2(x))/32
The initial velocity (v) is 90ft per second. The ball is pitched at an angle of x degrees with the horizontal. When x=26 degrees, the ball travels 200ft. At what other value of x will the ball travel 200ft?
X = 26 + 180 = 206 Deg.
CHECK:
Vo^2*sin2x/32
90^2*sin(412)/32 = 199.5 Deg.
Correction: R = 199.5 Ft. NOT Deg.
To find the other value of x where the ball will travel 200ft, we need to substitute the given values into the formula for the horizontal range and solve for x.
Given:
R(x) = 200ft
v = 90ft/s
Substituting these values into the formula for horizontal range:
200 = (90^2 * sin(2x))/32
Now, let's solve for x algebraically:
1. Multiply both sides of the equation by 32 to get rid of the denominator:
200 * 32 = 90^2 * sin(2x)
2. Now, divide both sides of the equation by 90^2 to isolate the sine function:
(200 * 32) / (90^2) = sin(2x)
3. Evaluate the left side of the equation:
(6400) / (8100) = sin(2x)
4. Simplify the expression:
8/9 = sin(2x)
5. Take the inverse sine (sin^(-1)) of both sides to find x:
sin^(-1)(8/9) = 2x
6. Divide both sides by 2 to solve for x:
x = sin^(-1)(8/9) / 2
Using a scientific calculator, we can find the value of sin^(-1)(8/9) which is approximately 53.13 degrees.
Therefore, the other value of x at which the ball will travel 200ft is:
x = 53.13 degrees