An object thrown into the air at an angle of 60° will have the same range as at 30° with the same speed. Group of answer choices
True
False
True.
For a given initial speed, the range of a projectile launched at an angle θ is given by the formula:
[ R = \frac{v^2 \sin(2\theta)}{g} ]
where ( R ) is the range, ( v ) is the initial speed, ( g ) is the acceleration due to gravity, and ( \theta ) is the launch angle.
The sine function has the property that ( \sin(2\theta) ) for ( \theta = 30° ) and ( \theta = 60° ) yields the same value:
[ \sin(60°) = \sin(120°) = \frac{\sqrt{3}}{2} ]
Thus, the ranges for both angles will be equal when launched with the same speed. Therefore, the statement is true.