for given angle of projection if time of flight is doubled horizontal range will increase to A FOUR TIMES B thrice C once D TWICE
For a projectile with
initial velocity=vi
projection angle = θ with horizontal
The time of flight
=2visin(θ)
If time is doubled with θ unchanged, vi is doubled.
From
range = vi²sin(2θ)/g
you can figure out the increase of the range when time (and vi) is doubled.
Double
To determine how the horizontal range changes when the time of flight is doubled for a given angle of projection, we can start by understanding the factors that affect the range of a projectile.
Horizontal range depends on two main factors: the initial velocity (speed) of the projectile and the time it spends in the air (time of flight). The angle of projection affects the vertical motion of the projectile (height reached) but does not directly influence the horizontal range.
The formula for the horizontal range of a projectile is:
Range = (Initial Velocity)^2 * sin(2θ) / gravitational acceleration
Where:
- Initial Velocity: The initial speed at which the projectile was launched.
- θ: The angle of projection.
- Gravitational acceleration: The acceleration due to gravity, which is constant (approximately 9.8 m/s² on Earth).
Now, let's evaluate each given option:
A) FOUR TIMES: If the time of flight is doubled, the range would increase by a factor of four. However, this is not correct based on the formula mentioned earlier.
B) thrice: If the time of flight is doubled, the range would increase by a factor of three. However, this is also not correct based on the formula.
C) once: If the time of flight is doubled, the range would increase by a factor of one. This suggests that there is no change in the range when the time of flight is doubled. This is the most likely correct answer since it aligns with the formula.
D) TWICE: If the time of flight is doubled, the range would increase by a factor of two. However, this contradicts the formula and is not correct either.
Therefore, the correct answer is C) once, which implies that the horizontal range remains the same when the time of flight is doubled for a given angle of projection.