Final answer:
To determine the time and height at which a cannonball will strike a wall, calculate the horizontal and vertical components of the initial velocity, then use these components to solve for the total time in flight and the vertical position of the cannonball at that time.
Step-by-step explanation:
To calculate the time it will take for the cannonball to strike the wall at a distance of 220 meters given an initial speed of 55 m/s at a launch angle of 40 degrees, we will use the horizontal component of the initial velocity, initial speed in the x-direction (Initial velocity cos(θ)), and the total horizontal distance traveled.
Find the time (t) needed for the horizontal travel:
Horizontal component of initial velocity, Vx = 55 m/s * cos(40°).
Since distance (d) = Vx * t, we solve for time:
t = 220 m / Vx.
To find the height at which it strikes the wall, we need to calculate the vertical position (y) at that time. We'll use the vertical component of the initial velocity (initial speed in the y-direction, Initial velocity sin(θ)) and the formula for the vertical motion:
Vertical component of initial velocity, Vy = 55 m/s * sin(40°).
The vertical position (y) at time t: y = Vy * t - (1/2) * g * t^2.
If y is greater than the height of the wall (30 m), the cannonball goes over the wall. If y equals the height of the wall, it strikes at exactly 30 m. If y is less than the height of the wall, that will be the height at which the cannonball strikes the wall.
Resolve the components:
- Vx = 55 m/s * cos(40°)
- Vy = 55 m/s * sin(40°)
Then plug these values into the respective formulas to find the time and the height at which the cannonball will strike the wall.