A stone popelled from a catalpult with the speed of 50m/s attained a height of 100m. Calculate the time of flight and angle of projection.
please solve it I don't understand
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To calculate the time of flight and angle of projection, we can use the equations of motion for projectile motion.
The first equation we will use relates the vertical displacement to the initial vertical velocity, time, and acceleration due to gravity:
h = u * t + (1/2) * g * t^2
where:
h = vertical displacement (100m in this case)
u = initial vertical velocity (0m/s at the highest point)
t = time of flight (what we want to find)
g = acceleration due to gravity (-9.8m/s^2)
Using the equation for vertical displacement, we can rearrange it to solve for time:
h = (1/2) * g * t^2
2h = g * t^2
t^2 = (2h) / g
t = sqrt((2h) / g)
Plugging in the values:
t = sqrt((2 * 100m) / -9.8m/s^2)
t = sqrt((-400m) / -9.8m/s^2)
t ≈ 6.41s
So, the time of flight is approximately 6.41 seconds.
Now, to calculate the angle of projection, we can use the equation for horizontal displacement. Since the stone was propelled horizontally from a catapult, there is no horizontal acceleration. The horizontal displacement is given by:
range = u * t * cos(theta)
where:
range = horizontal displacement (what we want to find)
u = initial velocity (50m/s in this case)
t = time of flight (6.41s)
theta = angle of projection (what we want to find)
Rearranging the equation to solve for the angle of projection:
range / (u * t) = cos(theta)
cos(theta) = range / (u * t)
theta = arccos(range / (u * t))
Since the stone reaches the same horizontal position as it was launched from, the range will be zero:
theta = arccos(0 / (50m/s * 6.41s))
theta = arccos(0)
theta = 90 degrees
Therefore, the angle of projection is 90 degrees.
To summarize:
Time of flight = 6.41 seconds
Angle of projection = 90 degrees