Final answer:
The initial speed of the projectile is 6.077 m/s.
Step-by-step explanation:
Calculation of Initial Speed of Projectile
In order to determine the initial speed of the projectile, we need to analyze the horizontal motion of the projectile since it was fired horizontally. In horizontal motion, there is no acceleration and the initial velocity is equal to the final velocity. Therefore, the initial speed of the projectile is equal to the horizontal distance it travels divided by the time it takes to travel that distance.
Using the given data, the projectile travels a horizontal distance of 2.335 m and was launched from a height of 0.726 m. We can use the time it takes for the projectile to hit the ground to calculate the initial speed. Since the projectile was launched horizontally, it will take the same amount of time to hit the ground as a projectile launched vertically from the same height. Using the equations of motion for vertical motion, we can calculate the time.
Using the equation:
h = 0.5 * g * t^2
where h is the initial height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time, we can solve for t:
0.726 = 0.5 * 9.8 * t^2
t^2 = 0.726/4.9
t = sqrt(0.726/4.9)
t = 0.384 s (rounded to 3 decimal places)
Now that we know the time, we can calculate the initial speed:
Initial speed = horizontal distance / time
Initial speed = 2.335 / 0.384
Initial speed = 6.077 m/s (rounded to 3 decimal places)