Final answer:
To calculate the height at which the net should be placed to catch the daredevil shot from a cannon, you must determine the time of flight using horizontal motion and then calculate the peak height reached using vertical motion, assuming initial height from the cannon is zero.
Step-by-step explanation:
To determine at what height above the cannon's mouth the net should be placed to catch the daredevil, we need to consider both horizontal and vertical motions separately, which are independent in projectile motion. The problem gives us the initial speed (26.9 m/s) and the launch angle (46.1°).
Firstly, we identify the time the daredevil is in midair. This is found by solving the horizontal motion. The horizontal velocity component (vx) can be found using the initial speed and the cosine of the launch angle.
Using the formula vx = v0 × cos(θ), we get:
vx = 26.9 m/s × cos(46.1°)
Then we find the time (t) using the formula s = vx × t, where s = 43.5 m is the distance to the net.
Next, we calculate the initial vertical velocity component (vy) using the formula vy = v0 × sin(θ).
With vy and known acceleration due to gravity (g = 9.81 m/s²), we can now find the height (h) part of the vertical motion using the formula h = vy × t - ½gt².
This height, which is the difference in height from the cannon's mouth to the peak of the projectile's arc, should be added to the cannon's initial height to determine at what height the net should be positioned. However, we were not given the cannon's initial height, so we assumed it to be zero, and the calculated height above the cannon's mouth would directly be the height at which to place the net.