a stone propelled from a catapult with a speed of 50m/s attains a height of 100m calculate the angle of projection
Indicate your subject in the "School Subject" box, so those with expertise in the area will respond to the question
What is its initial vertical speed Vo ?
v = Vo - 9.8 t
v = 0 at top
so
t = Vo/9.8
then height
h = Vo t - (9.8/2) t^2
100 = Vo^2/9.8 - (9.8/2) (Vo/9.8)^2
100 = Vo^2/(2*9.8)
Vo = 44.3 = speed sin theta
sin theta = 44.3/50
theta = 62.4 deg up from horizontal
Not correct
To calculate the angle of projection, we can use the following equation:
h = (v^2 * sin^2(θ)) / (2 * g)
Where:
h = maximum height reached by the projectile (in this case, 100m)
v = initial velocity of the projectile (in this case, 50 m/s)
θ = angle of projection
g = acceleration due to gravity (approximately 9.8 m/s^2)
Rearranging the equation, we have:
sin^2(θ) = (2 * g * h) / v^2
Taking the square root of both sides, we get:
sin(θ) = sqrt((2 * g * h) / v^2)
Now we can calculate the angle of projection.
First, let's calculate the value inside the square root:
(2 * 9.8 * 100) / (50^2) = 0.784
Taking the square root of 0.784, we get:
sin(θ) ≈ 0.885
To find the angle of projection, we need to take the inverse sine (sin^-1) of 0.885:
θ ≈ sin^-1(0.885)
Using a calculator or trigonometric table, we find that:
θ ≈ 62.5 degrees
Therefore, the angle of projection is approximately 62.5 degrees.