Daniyal Ahmad
Jul 19
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Jul 19
The height and range of a projectile are related mathematically through the equations of motion.
The height of a projectile at any given time can be calculated using the equation:
h(t) = v0*sin(θ)*t - (1/2)*g*t^2
where:
- h(t) is the height of the projectile at time t
- v0 is the initial velocity of the projectile
- θ is the angle of projection
- g is the acceleration due to gravity
- t is the time elapsed since the projectile was launched
The range of a projectile, which is the horizontal distance it travels before hitting the ground, can be calculated using the equation:
R = v0*cos(θ)*t
where:
- R is the range of the projectile
- v0 is the initial velocity of the projectile
- θ is the angle of projection
- t is the time elapsed since the projectile was launched
By combining these two equations, we can see that the height and range of a projectile are related through the initial velocity, angle of projection, and time of flight. The maximum range of a projectile is achieved when the angle of projection is 45 degrees.
The height of a projectile at any given time can be calculated using the equation:
h(t) = v0*sin(θ)*t - (1/2)*g*t^2
where:
- h(t) is the height of the projectile at time t
- v0 is the initial velocity of the projectile
- θ is the angle of projection
- g is the acceleration due to gravity
- t is the time elapsed since the projectile was launched
The range of a projectile, which is the horizontal distance it travels before hitting the ground, can be calculated using the equation:
R = v0*cos(θ)*t
where:
- R is the range of the projectile
- v0 is the initial velocity of the projectile
- θ is the angle of projection
- t is the time elapsed since the projectile was launched
By combining these two equations, we can see that the height and range of a projectile are related through the initial velocity, angle of projection, and time of flight. The maximum range of a projectile is achieved when the angle of projection is 45 degrees.
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Google Gemini AI
Jul 19
The height and range of a projectile are related mathematically by the following equations:
- Height (h):
- h = (v^2 - sin^2(theta)) / (2 - g)
- Range (R):
- R = (v^2 - sin(2 - theta)) / g
where:
- v is the initial velocity of the projectile
- theta is the angle of projection (measured from the horizontal)
- g is the acceleration due to gravity
- Height (h):
- h = (v^2 - sin^2(theta)) / (2 - g)
- Range (R):
- R = (v^2 - sin(2 - theta)) / g
where:
- v is the initial velocity of the projectile
- theta is the angle of projection (measured from the horizontal)
- g is the acceleration due to gravity
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