# High School Physics : Motion and Mechanics

## Example Questions

### Example Question #1 : Understanding Motion In Two Dimensions

A ball rolls off of a table with an initial horizontal velocity of . If the table is  high, what is the final vertical velocity?

Explanation:

The problem states that the initial velocity is only in the horizontal direction; the initial vertical velocity is zero. We now know initial velocity, acceleration, and distance traveled.

Remember, even though the distance it will travel is , its displacement will be  as it moves in the downward direction.

Using these values and the appropriate motion equation, we can solve for the final velocity. The best equation to use is:

Use the given values to find the final velocity.

Because we just took the square root of a number, we got an absolute value for our ; however, velocity is a vector and can be either positive or negative depending on direction. Because the ball is headed downward, the final velocity should correctly be . Remember that a negative number squared gives a positive value, just like a positive number.

### Example Question #6 : Understanding Motion In Two Dimensions

A ball rolls off of a table with an initial horizontal velocity of . If the table is  high, how far from the table will it land?

Explanation:

We can solve for the horizontal distance using only the horizontal velocity: .

We are given the value of , but we need to find the time. Time in the air will be determined by the vertical components of the ball's motion.

We know the height of the table, the initial velocity, and gravity. Using these values with the appropriate motion equation, we can solve for the time.

The best equation to use is:

We can use our values to solve for the time. Keep in mind that the displacement will be negative because the ball is traveling in the downward direction!

Now we have both the time and the horizontal velocity. Use the original equation to solve for the distance.

### Example Question #1 : Understanding Motion In Two Dimensions

A man stands on a tall ladder of height . He leans over a little too far and falls off the ladder. What would be the best way to describe his fall?

We would need to know his mass in order to determine the type of motion

Circular motion

Parabolic motion

One-dimensional motion

We would need to know air resistance in order to determine his type of motion

Parabolic motion

Explanation:

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.

### Example Question #1 : Understanding Motion In Two Dimensions

A cannon on level ground fires a cannon ball at  at  above the horizontal. What is the final horizontal velocity?

Explanation:

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.

### Example Question #2 : Understanding Motion In Two Dimensions

A cannon on level ground fires a cannon ball at  at  above the horizontal. What is the initial vertical velocity?

Explanation:

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.

### Example Question #41 : Linear Motion

A cannon on level ground fires a cannon ball at  at  above the horizontal. How high does the cannon ball go?

Explanation:

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.

### Example Question #41 : Motion And Mechanics

A cannon on level ground fires a cannon ball at  at  above the horizontal. How long does it take the ball to reach its maximum height?

Explanation:

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.

### Example Question #41 : Motion And Mechanics

A cannon on level ground fires a cannon ball at  at  above the horizontal. What is the total time the ball is in the air?

Explanation:

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.

### Example Question #42 : Linear Motion

A cannon on level ground fires a cannon ball at  at  above the horizontal. What is the total horizontal distance that the cannon ball travels?

Explanation:

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.

### Example Question #41 : Linear Motion

Peter walks  north of east. What is his total displacement along the y-axis?

Explanation:

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 .