The path of a projectile fired at an inclination t0 to the horizontal with initial velocity v feet per second is a parabola. The horizontal distance R, in feet, that the projectile travels is given by R = v2sin(2t)/32.2. What is R if v = 152 and t = 74? Give your answer to the nearest thousandth?
To find the horizontal distance traveled by the projectile, we can use the given equation:
R = v^2 * sin(2t) / 32.2
We are given that v = 152 and t = 74, so we can substitute these values into the equation:
R = (152^2) * sin(2*74) / 32.2
To evaluate this expression, we need to calculate sin(2*74).
Step 1: Calculate 2*74
2*74 = 148
Step 2: Find the sine of 148
sin(148) = -0.766
Now we substitute this value back into the original equation:
R = (152^2) * (-0.766) / 32.2
Step 3: Calculate 152^2
152^2 = 23104
Now we can substitute the values and evaluate the expression:
R = 23104 * (-0.766) / 32.2
Step 4: Perform the multiplications and division
R ≈ -549.519
Finally, we round R to the nearest thousandth:
R ≈ -549.519, rounded to the nearest thousandth is -549.519 feet.