# High School Physics : Understanding Motion in Two Dimensions

## Example Questions

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### 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, how long will it take to hit the ground?

Explanation:

The problem gives us the initial horizontal velocity. This velocity will only affect the distance the ball travels in the horizontal direction; it will have no effect on the time the ball is in the air. Since there is no angle of trajectory, the ball has no initial vertical velocity.

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!

### Example Question #2 : 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 horizontal velocity?

Explanation:

One of the key concepts of parabolic motion in freefall is that the horizontal velocity, , does not change. In order for velocity to change, there must be an acceleration. If an object is accelerating, then there must be a force acting on the object. The only force on the object during freefall is gravity, which acts in the vertical direction and cannot affect the horizontal velocity.

Since our given , our .

### Example Question #3 : 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 angle the ball will make above the horizontal as it strikes the ground?

Explanation:

In order for us to find the final angle, we need to find the final horizontal and vertical components.

The only force acting on the ball while in the air is gravity. Since gravity acts in the vertical direction, there is no force in the horizontal direction. This means that the horizontal velocity will not change.

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.

Now that we know the horizontal and vertical components of the final velocity, we can solve for the angle by considering the components are legs of a right triangle. Using trigonometric identities, we can solve for the angle.

Using our horizontal and vertical velocities, we can calculate the angle.

### Example Question #4 : Understanding Motion In Two Dimensions

A ball rolls off of a table with an initial horizontal velocity of . If the table is  high, what will be its final total speed?

Explanation:

In order for us to find the final resultant speed, we need to find the final horizontal and vertical components.

The only force acting on the ball while in the air is gravity. Since gravity acts in the vertical direction, there is no force in the horizontal direction. This means that the horizontal velocity will not change.

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.

Now that we know the final velocity in both the horizontal and vertical directions, we can use the Pythagorean theorem to solve for the total velocity.

### Example Question #5 : 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 #5 : 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?

Parabolic motion

One-dimensional motion

Circular motion

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

We would need to know his mass in order to determine the 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 #42 : Motion And Mechanics

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 #9 : 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 #43 : Motion And Mechanics

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