To determine the time the cannonball will stay in the air when fired straight up, we can use the fact that the time taken to reach the maximum height is equal to the time taken to fall back to the ground.
When the cannonball is fired straight up, it reaches a maximum height and then falls back down. At the highest point, its vertical velocity becomes zero before it starts falling due to the acceleration due to gravity.
To find the time taken to reach the maximum height, we can use the equation:
v = u + at
Where: v = final velocity (0 m/s at the highest point) u = initial velocity (50 m/s) a = acceleration due to gravity (-9.8 m/s², taking the negative sign as it acts opposite to the initial velocity) t = time
Rearranging the equation, we get:
t = (v - u) / a
Substituting the values:
t = (0 - 50) / (-9.8)
t = 50 / 9.8
t ≈ 5.1 seconds
Therefore, the cannonball will stay in the air for approximately 5.1 seconds before falling back down, assuming no air resistance.