Final answer:
The question pertains to the calculation of range and time of flight for a cannonball fired at an angle in Physics, specifically related to the concept of projectile motion. Formulas involving the initial velocity, angle of launch, and gravity are used to determine these values.
Step-by-step explanation:
The question involves calculating the range and the time of flight of a cannonball that is fired at an angle above the horizontal plane. This scenario is an example of projectile motion, which is a common topic in high school Physics. The range refers to how far the cannonball travels horizontally before it hits the ground, and time of flight is the total time the cannonball remains in the air.
To solve part (A) and find the range, we would use the following formula:
- Range (R) = (v² * sin(2θ)) / g
where v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. We must take the sine of twice the angle because the range formula depends on the initial velocity components in both the x (horizontal) and y (vertical) direction.
For part (B), the time of flight (T) can be found using the following steps:
- Calculate the initial vertical velocity (v₀y = v * sin(θ)).
- Calculate the time to reach the maximum height (t = v₀y / g).
- Double the time to account for both the ascent and descent since the time to go up is the same as the time to come down (T = 2 * t).