What are the possible angles of projection with the same velocity to have same range
Answers
Answered by
6
The following equation is used to determine the range.
Range = v^2/g * sin 2 θ
In trigonometry class, you learn the following identity.
Sin 2 θ = 2 * sin θ * cos θ
Range = v^2/g * (2 * sin θ * cos θ)
For range to be the same at the same velocity, the product of sin θ1 * cos θ2 must be the same number. For this to be true, the angles must the angles of a right triangle. To see if this is true, let the velocity be 50 m/s and the angles be 30˚ and 60˚.
Range = 50^2/ 9.8 * (2 * sin 30 * cos 30) = 220.9248479
Range = 50^2/9.8 * (2 * sin 60 * cos 60) = 220.9248479
The range is the same when the sum of the angles is 90˚.
2 * sin 50 * cos 50 = 0.984
2 * sin 40 * cos 40 = 0.984
The range is the same when the angles are from a right triangle!
When the angle is 45˚, the range is the maximum amount.
2 * sin 45 * cos 45 = 1
Range = v^2/g * (2 * sin 45 * cos 45) = v/^2/g
This the maximum value of this equation. I hope my work and explanations have helped you to understand how to solve this problem
Range = v^2/g * sin 2 θ
In trigonometry class, you learn the following identity.
Sin 2 θ = 2 * sin θ * cos θ
Range = v^2/g * (2 * sin θ * cos θ)
For range to be the same at the same velocity, the product of sin θ1 * cos θ2 must be the same number. For this to be true, the angles must the angles of a right triangle. To see if this is true, let the velocity be 50 m/s and the angles be 30˚ and 60˚.
Range = 50^2/ 9.8 * (2 * sin 30 * cos 30) = 220.9248479
Range = 50^2/9.8 * (2 * sin 60 * cos 60) = 220.9248479
The range is the same when the sum of the angles is 90˚.
2 * sin 50 * cos 50 = 0.984
2 * sin 40 * cos 40 = 0.984
The range is the same when the angles are from a right triangle!
When the angle is 45˚, the range is the maximum amount.
2 * sin 45 * cos 45 = 1
Range = v^2/g * (2 * sin 45 * cos 45) = v/^2/g
This the maximum value of this equation. I hope my work and explanations have helped you to understand how to solve this problem
Similar questions