Final answer:
The time in the air and maximum height of a cannonball launched at an angle can be found using the formulas for projectile motion with initial conditions, accounting for the final landing height being lower than the starting point.
Step-by-step explanation:
The question pertains to the time of flight and maximum height attained by a cannonball in projectile motion. To determine these parameters, we can use the formulas for projectile motion. Given that the cannonball is launched with an initial velocity of 145.0 m/s at an angle of 35 degrees and lands 150 meters lower than its initial height, we must consider the vertical component of the motion separately from the horizontal.
For finding the time in the air, we could use the following equation in combination with quadratic formulas to solve for time (t):
y = y0 + v0yt - ½gt2
where y is the final vertical position (-150 m), y0 is the initial vertical position (0 m), v0y is the initial vertical velocity (v0sinθ), and g is the acceleration due to gravity (9.81 m/s2). We must apply the quadratic formula to solve for the time since the cannonball lands below its initial height.
For calculating the maximum height (H), the equation would be:
H = y0 + (v0y2)/(2g)
This problem neglects air resistance, which simplifies the calculations. However, remember that these equations assume a constant acceleration due to gravity and do not account for factors like air resistance or Earth's rotation.