A daredevil is shot out of a cannon at an angle of 31.3 degrees to the horizontal with an initial speed of 27.7 m/s. A net is positioned at a horizontal distance of 36.9 m from the cannon. The acceleration due to gravity is 9.81 m/s².

At what height above the cannon’s mouth should the net be placed in order to catch the daredevil? Answer in units of meters.

A) 31.3
B) 27.7
C) 36.9
D) 9.81

To find the height at which the net should be placed to catch the daredevil, we calculate the time of flight using the horizontal range and then use the vertical motion equation with the initial vertical velocity and the time of flight. The final vertical position gives us the required height of the net, which is not one of the provided options (A, B, C, D).

Explanation:

To calculate the height at which the net should be placed to catch the daredevil shot out of a cannon, we can use the projectile motion equations. We are given the initial velocity (27.7 m/s), the angle of projection (31.3 degrees), and the horizontal distance (36.9 m). The acceleration of gravity is 9.81 m/s2.

We start by finding the time of flight using the horizontal motion equation:

Range (R) = (initial velocity * cos(angle)) * time
36.9 m = (27.7 m/s * cos(31.3°)) * time
time = 36.9 m / (27.7 m/s * cos(31.3°))

With the time of flight calculated, we then find the vertical component of the initial velocity:

Vertical velocity = 27.7 m/s * sin(31.3°)

Using the vertical motion equation:

Final vertical position = Initial vertical position + (Vertical velocity * time) - (0.5 * g * time2)

The initial vertical position is 0 since we measure the height relative to the cannon's mouth. The final vertical position is where the net should be. We compute this value to find the answer.

Learn more about Projectile Motion here:

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