a stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight and the angle of projection
vertical problem:
v = Vi - 9.81 t
v = 0 at the top
t = Vi/9.81 at the top which is 100 meters
h = Vi t - 4.9 t^2
100 = Vi^2/9.81 - .5*9.81 (Vi^2/9.81^2)
100 = .5Vi^2/9.81
Vi = 44.3 m/s
T = angle up from horizontal
sin T = 44.3/50
T = 62.4 degrees
t = 2 * Vi/9.81 = 2*44.3/9.81 = 9.03 seconds
I didn't really understand ur formula and ur parameters but it is OK . the answer was correct.
To calculate the time of flight and the angle of projection of a stone propelled from a catapult, we can use the equations of motion.
Step 1: Calculate the time of flight.
Using the equation of motion for vertical displacement:
h = (u^2 sin^2 θ)/(2g)
Where:
h = vertical displacement (100m in this case)
u = initial velocity (50 m/s in this case)
θ = angle of projection
g = acceleration due to gravity (9.8 m/s^2)
Rearranging the equation to solve for time (t):
t = (2usinθ)/g
Substituting the known values into the equation, we get:
t = (2 * 50 * sinθ)/9.8
Step 2: Calculate the angle of projection.
Using the equation of motion for horizontal displacement:
Range (R) = (u^2 sin2θ)/g
Where:
R = range
u = initial velocity (50 m/s in this case)
θ = angle of projection
g = acceleration due to gravity (9.8 m/s^2)
Rearranging the equation to solve for α (angle of projection):
sin2θ = (gR)/(u^2)
Taking the arcsine of both sides to isolate θ:
2θ = arcsin((gR)/(u^2))
θ = 1/2 * arcsin((gR)/(u^2))
Substituting the known values into the equation, we get:
θ = 1/2 * arcsin((9.8 * 100)/(50^2))
Now we can calculate t and θ using the equations:
t = (2 * 50 * sinθ)/9.8
θ = 1/2 * arcsin((9.8 * 100)/(50^2))
Calculating t:
t = (2 * 50 * sin(θ))/9.8
t = (100 * sin(θ))/9.8
Calculating θ:
θ = 1/2 * arcsin((9.8 * 100)/(50^2))
θ = 1/2 * arcsin(0.392)
θ ≈ 11.25 degrees
Therefore, the time of flight of the stone is approximately (100 * sin(11.25))/9.8 seconds and the angle of projection is approximately 11.25 degrees.