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So our equation for the launch angle of the projectile is 𝜃 equals the inverse sin of the square root of two 𝑔ℎ divided by 𝑉. All that's left to do is to substitute our known values of 𝑉, 𝑔, and ℎ into this equation to calculate 𝜃. The question tells us that the initial speed of the projectile is 28 meters per second.

The cannonball launched at a 45-degree angle had the greatest range. The cannonball launched at a 60-degree angle had the highest peak height before falling. The cannonball launched at the 30-degree angle reached the ground first.

For ideal projectile motion, which starts and ends at the same height, maximum range is achieved when the firing angle is 45°.

What is the projectile-motion equation? The projectile-motion equation is s(t) = −½ gx2 + v0x + h0, where g is the constant of gravity, v0 is the initial velocity (that is, the velocity at time t = 0), and h0 is the initial height of the object (that is, the height at of the object at t = 0, the time of release).

The sine function reaches its largest output value, 1, with an input angle of 90 degrees, so we can see that for the longest-range punts 2θ = 90 degrees and, therefore, θ = 45 degrees. A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees.

To calculate projectile motion at an angle, first resolve the initial velocity into horizontal and vertical components. The x−component (horizontal) is: vx=vcosθ. The y−component (vertical) is: vy=vsinθ. Analysis of projectile motion involves dealing with two motions independently.

Launch angles closer to 45 ° 45\degree 45° give longer maximum horizontal distance (range) if initial speed is the same (see figure 5 above). These launches have a better balance of the initial velocity components that optimize the horizontal velocity and time in air (see figure 4).

Answer and Explanation: 45 degrees is the optimal angle because it is the optimal combination of forward and upward components of velocity that give the projectile sufficient forward velocity and hang time to produce the greatest range.

So our equation for the launch angle of the projectile is 𝜃 equals the inverse sin of the square root of two 𝑔ℎ divided by 𝑉. All that's left to do is to substitute our known values of 𝑉, 𝑔, and ℎ into this equation to calculate 𝜃. The question tells us that the initial speed of the projectile is 28 meters per second.

The cannonball launched at a 45-degree angle had the greatest range. The cannonball launched at a 60-degree angle had the highest peak height before falling. The cannonball launched at the 30-degree angle reached the ground first.

For ideal projectile motion, which starts and ends at the same height, maximum range is achieved when the firing angle is 45°.

What is the projectile-motion equation? The projectile-motion equation is s(t) = −½ gx2 + v0x + h0, where g is the constant of gravity, v0 is the initial velocity (that is, the velocity at time t = 0), and h0 is the initial height of the object (that is, the height at of the object at t = 0, the time of release).

The sine function reaches its largest output value, 1, with an input angle of 90 degrees, so we can see that for the longest-range punts 2θ = 90 degrees and, therefore, θ = 45 degrees. A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees.

To calculate projectile motion at an angle, first resolve the initial velocity into horizontal and vertical components. The x−component (horizontal) is: vx=vcosθ. The y−component (vertical) is: vy=vsinθ. Analysis of projectile motion involves dealing with two motions independently.

Launch angles closer to 45 ° 45\degree 45° give longer maximum horizontal distance (range) if initial speed is the same (see figure 5 above). These launches have a better balance of the initial velocity components that optimize the horizontal velocity and time in air (see figure 4).

Answer and Explanation: 45 degrees is the optimal angle because it is the optimal combination of forward and upward components of velocity that give the projectile sufficient forward velocity and hang time to produce the greatest range.