A canon is angled at 45º and fires a canon ball at 100 m/s. How long will it take the canon to reach it's maximum height?
To find the time it takes for the cannonball to reach its maximum height, we need to break down the motion of the cannonball.
Step 1: Determine the initial vertical velocity of the cannonball.
The cannonball is fired at an angle of 45 degrees, but we need to analyze its vertical motion separately. The initial vertical velocity (Viy) can be found using the formula Viy = V * sin(θ), where V is the initial velocity (100 m/s) and θ is the angle of projection (45 degrees).
Viy = 100 m/s * sin(45º)
= 100 m/s * 0.7071
≈ 70.71 m/s
Step 2: Calculate the time to reach maximum height.
The time it takes for an object to reach its maximum height during vertical motion can be found using the formula t = Viy / g, where g is the acceleration due to gravity (approximately 9.8 m/s²).
t = 70.71 m/s / 9.8 m/s²
≈ 7.23 seconds
Therefore, it will take approximately 7.23 seconds for the cannonball to reach its maximum height.