Final answer:
To solve the problem, we can use the kinematic equation for horizontal motion. The cannonball is launched horizontally, so its initial vertical velocity is 0 m/s. Using the equation d = Vit + (1/2)at^2 and substituting the given values, we can solve for time and find that the cannonball takes approximately 3.19 seconds to hit the ground.
Step-by-step explanation:
To solve this problem, we can use the kinematic equation for horizontal motion. The cannonball is launched horizontally, so its initial vertical velocity is 0 m/s. Since it is launched from a 50 m tall cliff, the initial vertical displacement is 50 m. We can use the equation:
d = Vit + (1/2)at^2
Given that the initial vertical velocity is 0 m/s, the acceleration due to gravity is -9.8 m/s^2, and the initial vertical displacement is -50 m (taking downwards as the negative direction), we can substitute these values into the equation and solve for time:
-50 = 0t + (1/2)(-9.8)t^2
Simplifying the equation, we have:
-4.9t^2 = -50
To solve for t, we divide both sides by -4.9:
t^2 = 10.2
t = sqrt(10.2) ≈ 3.19 s
Therefore, the cannonball takes approximately 3.19 seconds to hit the ground.