The man's fall will be parabolic as there will be both horizontal and vertical components. His vertical component of the fall will be standard free-fall caused by his acceleration due to gravity. His horizontal component of the fall will come from him "leaning too far" in one direction. Even a small horizontal velocity will create a horizontal trajectory.

This is why when people lean and fall off of ladders they either try to grab onto the ladder (try to negate their horizontal velocity) or fall a small distance away from the base of the ladder.

Remember that the velocity in the horizontal direction stays constant through the projectile's motion. There is no force in the horizontal direction, only in the vertical direction. That means the initial and final horizontal velocities will be the same.

To find our , we need to use cosine trigonometry, with the horizontal velocity as the adjacent side and the total initial velocity as the hypotenuse.

We are given the total initial velocity and the angle of the initial trajectory. Using these values, we can use trigonometry to solve for the initial vertical velocity.

We will need to use sine, with the vertical velocity as the opposite side and the total velocity as the hypotenuse.

To find the height of the projectile, we can use the appropriate kinematics equation:

We know that the final velocity at the maximum height will be zero, and we also know the acceleration due to gravity. Before we can use the equation, however, we must solve for the initial vertical velocity. We are given the total initial velocity and the angle of the initial trajectory. Using these values, we can use trigonometry to solve for the initial vertical velocity.

Now that we know the initial vertical velocity, we can return to the kinematics equation to solve for the final displacement.

To find the time for the projectile to reach its maximum height, we can use the appropriate kinematics equation:

We know that the final velocity at the maximum height will be zero, and we also know the acceleration due to gravity. Before we can use the equation, however, we must solve for the initial vertical velocity. We are given the total initial velocity and the angle of the initial trajectory. Using these values, we can use trigonometry to solve for the initial vertical velocity.

Now that we know the initial vertical velocity, we can return to the kinematics equation to solve for the time.

To find the total time, we can solve for the time to reach the peak and then double this value to find the total time.

To find the time for the projectile to reach its maximum height, we can use the appropriate kinematics equation:

We know that the final velocity at the maximum height will be zero, and we also know the acceleration due to gravity. Before we can use the equation, however, we must solve for the initial vertical velocity. We are given the total initial velocity and the angle of the initial trajectory. Using these values, we can use trigonometry to solve for the initial vertical velocity.

Now that we know the initial vertical velocity, we can return to the kinematics equation to solve for the time.

Double this value to find the total flight time.

To solve for the horizontal distance we can use the simple formula for velocity, since there is no acceleration in the horizontal direction.

This leaves us two distinct variables:  and .

To find our , we need to use cosine.

To find the time, we can solve for the time to reach the peak and then double this value to find the total time.

To find the time for the projectile to reach its maximum height, we can use the appropriate kinematics equation:

We know that the final velocity at the maximum height will be zero, and we also know the acceleration due to gravity. Before we can use the equation, however, we must solve for the initial vertical velocity. We are given the total initial velocity and the angle of the initial trajectory. Using these values, we can use trigonometry to solve for the initial vertical velocity.

Now that we know the initial vertical velocity, we can return to the kinematics equation to solve for the time.

Double this value to find the total flight time.

Now that we know our total time and horizontal velocity, we can return to the velocity equation to solve for the distance traveled.

Start by drawing a picture.

By traveling both north and east, Peter has displacement along both the x-axis and the y-axis. Recognize that this makes a right triangle.

We can solve for the y-axis displacement by using trigonometry.

In this case, we know the angle and the hypotenuse. The y-displacement is opposite the angle.

Multiply both sides by  and solve.

Since we are solving for the displacement, we need to include the direction. The displacement is .

Start by drawing a picture.

By traveling both north and east, Peter has displacement along both the x-axis and the y-axis. Recognize that this makes a right triangle.

We can solve for the x-axis displacement by using trigonometry.

In this case, we know the angle and the hypotenuse. The x-displacement is adjacent to the angle.

Multiply both sides by  and solve.

Since we are solving for the displacement, we need to include the direction. The displacement is .

When a projectile is launched at an angle, the result is an initial velocity with both horizontal and vertical components.

Once these initial components are determined, we can find how they change during flight. The only thing capable of changing a given velocity is an outside force (Newton's first law). The only force acting on the ball in the air is gravity, which serves to decrease the positive vertical velocity. There are no forces in the horizontal direction. Since gravity acts perpendicular to the horizontal velocity, it has no effect and cannot change the horizontal velocity value. As a result, the horizontal velocity remains constant at all points during projectile motion, even though the vertical velocity will change due to gravity.