A Stone propelled from a catapult with a speed of 50m/s attains a height of 100m. Calculate the following 1 The time flight, 2 The angle of projection, 3 The. range.
To felix,Plsss number one explain the formulae,and r-scott plss explain in details
1 ... time up equals time down equals T ...100 = 1/2 g T^2
... the flight time is ... 2 T
2 ... 50 sin(Θ) = g T
3 ... range = 2 * T * 50 * cos(Θ)
vertical problem first
No need for anything but g = 9.81 m/s^2 and max height is 100 m
We will get the initial vertical speed Vi
v = Vi - 9.81 t
v = 0 at top
Vi = 9.81 t
h = Hi + Vi t - 4.9 t^2
100 = 0 + 9.81 t^2 - 4.9 t^2
4.9 t^2 = 100
t = 4.52 seconds upward (total of 9.04 in air)
Vi = 9.81*4.52 = 44.3 m/s initial speed upward
so
sin theta = 44.3 / 50
theta = 62.4deg above horizontal
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Horizontal problem
goes at 50 cos 62.4 for 9.04 seconds
u = 23.2 m/s and x = 209 meters
To calculate the time of flight, angle of projection, and range of a stone propelled from a catapult, we can use the equations of projectile motion. Projectile motion is the motion of an object that is launched into the air with an initial velocity and follows a curved path due to the force of gravity.
1. Time of Flight:
The time of flight is the total amount of time it takes for the stone to reach its maximum height and return to the same height. We can use the equation:
time of flight = 2 * (vertical component of initial velocity) / (acceleration due to gravity)
The vertical component of initial velocity can be found using the initial speed and the angle of projection. In this case, the initial speed is 50 m/s, and the angle of projection is unknown. Let's call the angle of projection "θ". We can use trigonometry to find the vertical component as:
vertical component of initial velocity = initial speed * sin(θ)
Now, substituting the values into the equation:
time of flight = 2 * (50 * sin(θ)) / (9.8)
2. Angle of Projection:
Since we are given the initial speed and the height reached, we can find the angle of projection using the equation:
height = (vertical component of initial velocity)^2 / (2 * acceleration due to gravity)
Substituting the known values:
100 = (50 * sin(θ))^2 / (2 * 9.8)
Now, solving for θ:
θ = arcsin(sqrt((100 * 2 * 9.8) / (50^2)))
3. Range:
The range is the horizontal distance covered by the stone. We can use the formula:
range = (horizontal component of initial velocity) * time of flight
The horizontal component of initial velocity can be found using the initial speed and the angle of projection:
horizontal component of initial velocity = initial speed * cos(θ)
Now, substituting the known values:
range = (50 * cos(θ)) * time of flight
By calculating the time of flight in step 1 and substituting it into the equation above, we can find the range.