A proiettile is fired with an initial velocity of 100m/a at an Angle of 30degree on the Horizonte calculate the range
E is 786
assume you mean 100 m/s
Vertical problem first:
Vi = 100 sin 30 = 50 m/s
v= Vi - g t = 50 - 9.81 t
v = 0 at top
9.81 t = 50 at top
t = 50/9.81 = 5.1 s to top
that is 10.2 s in the air including the fall
now the horizontal problem
u = 100 cos 30 = 86.6 m/s
t = 10.2 s
so range = 86.6* 10.2 = 883 meters
To calculate the range of a projectile fired at an angle, you can use the formula:
Range = (Initial Velocity^2 * sin(2θ)) / g
Where:
Initial Velocity = 100 m/s (given in the question)
θ (angle of projection) = 30 degrees (given in the question)
g (acceleration due to gravity) = 9.8 m/s^2 (standard value)
Let's substitute the given values into the formula and calculate the range:
Range = (100^2 * sin(2*30)) / 9.8
First, let's calculate sin(2*30):
sin(2*30) = sin(60) = √3 / 2
Now, substitute the value into the formula:
Range = (100^2 * (√3 / 2)) / 9.8
Calculate the result:
Range = (10000 * √3) / 19.6
Range ≈ 541.27 meters
Therefore, the range of the projectile is approximately 541.27 meters.
To calculate the range of a projectile fired at an angle, you can use the following equation:
Range = (V₀² * sin(2θ)) / g
where:
V₀ is the initial velocity of the projectile
θ is the launch angle
g is the acceleration due to gravity (approximately 9.8 m/s²)
In this case, the initial velocity (V₀) is given as 100 m/s and the launch angle (θ) is 30 degrees.
First, convert the launch angle from degrees to radians:
θ_rad = θ * π / 180
θ_rad = 30 * π / 180
θ_rad = π / 6 rad
Next, plug the values into the equation:
Range = (100² * sin(2 * (π / 6))) / 9.8
Now, calculate the range:
Range = (10,000 * sin(2 * (π / 6))) / 9.8
Range = (10,000 * sin(π / 3)) / 9.8
Range = (10,000 * √3/2) / 9.8
Range = (10,000 * 1.73) / 9.8
Range ≈ 17398.98 / 9.8
Range ≈ 1775.5 meters
Therefore, the range of the projectile is approximately 1775.5 meters.