The question gives the total initial velocity, but we will need to find the vertical component.

To find the vertical velocity we use the equation .

We can plug in the given values for the angle and initial velocity to solve.

The given initial velocity is at an angle, so we have to use some trigonometric functions to break it into horizontal and vertical components.

Effectively, the initial velocity becomes the hypotenuse of a right triangle with the horizontal velocity becoming the base and the vertical velocity becoming the height. To find the vertical velocity, we use the relationship between the hypotenuse and the opposite side.

Use the given initial velocity and angle to solve for the vertical velocity.

The given initial velocity is at an angle, so we have to use some trigonometric functions to break it into horizontal and vertical components.

Effectively, the initial velocity becomes the hypotenuse of a right triangle with the horizontal velocity becoming the base and the vertical velocity becoming the height. To find the horizontal velocity, we use the relationship between the hypotenuse and the adjacent side.

Use the given initial velocity and angle to find the horizontal velocity.

In a problem with parabolic motion, your first step should always be to break the given velocity into its horizontal and vertical components. 

Use cosine to find the initial horizontal velocity.

We are given the initial velocity and angle.

Use these values with sine to find the initial vertical velocity.

The question is asking for the velocity at the maximum height or, in our terms, the top of the parabola. At the top of the parabola the vertical velocity will be zero, but the horizontal velocity will remain constant. To find the total velocity, we normally use the Pythagorean Theorem with the horizontal and vertical velocities.

Since we know that the vertical velocity is zero, however, we can see that the total velocity will simply be equal to the horizontal velocity.

Even though the problem gives us an initial velocity, we need to break it down into horizontal and vertical components.

Use the sine function with the initial velocity and angle to find the vertical velocity.

Remember that the vertical velocity at the highest point of a parabola is zero. We know the initial and final velocities, and the acceleration of gravity. Using these values in the appropriate motion equation, we can find the height that the rock travels.

Remember,  only tells us the CHANGE in the vertical direction. Since the rock started at the top of a  building, it rose an extra  after it was thrown. Its highest point it is  above the ground.

The given velocity won't help us much here. We need to break it down into horizontal and vertical components. 

Use the sine function with the initial velocity and angle to find the vertical velocity.

Now we need to work on finding the time in the air. To do this, we need to break the rock's path into two parts. The first part is the time that the rock is rising to its maximum height, and the second part is the time that it is falling from the highest point to the ground.

For the first part, we can assume that the final vertical velocity is zero, since this will be the top of the parabola. Using the initial velocity, final velocity, and gravity, we can solve for the time to travel this portion of the path.

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This is the time that the rock is traveling upward. Now we need to focus on the time that the rock travels downward. We don't know the final velocity at the end of the parabola, so we can't use the equation from the first part. If we can find the total height of the parabola, we can use a different equation to solve for time.

Remember that the vertical velocity at the highest point of a parabola is zero. Now that we know the initial vertical velocity, we can plug this into an equation to solve for the distance that the rock travels from its maximum height to the original height.

Remember,  only tells us the CHANGE in height. Since the rock started at the top of a  tall building, if it rose an extra , then at its highest point it is  above the ground.

This means that our  for the second equation will be  (the change in height is negative because it travels downward.) Use this total distance and the velocity at the top of the peak (zero) to solve for the time that the rock travels down.

Finally, add the two times together to find the total time in flight.

To find the horizontal distance, we will need to use the horizontal velocity and the total time that the rock is in the air. We can easily find the horizontal velocity by using the cosine function and the initial velocity and angle.

There is no horizontal acceleration, so the velocity will be constant. This means our equation for distance will be simply:

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We know , but now we need to find the time the rock is in the air.

Use the sine function with the initial velocity and angle to find the vertical velocity.

We need to break the rock's path into two parts. The first part is the time that the rock is rising to its maximum height, and the second part is the time that it is falling from the highest point to the ground.

For the first part, we can assume that the final vertical velocity is zero, since this will be the top of the parabola. Using the initial velocity, final velocity, and gravity, we can solve for the time to travel this portion of the path.

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This is the time that the rock is traveling upward. Now we need to focus on the time that the rock travels downward. We don't know the final velocity at the end of the parabola, so we can't use the equation from the first part. If we can find the total height of the parabola, we can use a different equation to solve for time.

Remember that the vertical velocity at the highest point of a parabola is zero. Now that we know the initial vertical velocity, we can plug this into an equation to solve for the distance that the rock travels from its maximum height to the original height.

Remember,  only tells us the CHANGE in height. Since the rock started at the top of a  tall building, if it rose an extra , then at its highest point it is  above the ground.

This means that our  for the second equation will be  (the change in height is negative because it travels downward.) Use this total distance and the velocity at the top of the peak (zero) to solve for the time that the rock travels down.

Finally, add the two times together to find the total time in flight.

Now that we have finally found our time, we can plug that back into the equation from the beginning of the problem:

Use the time and horizontal velocity to find the total horizontal distance.

First, break our given velocity into its horizontal and vertical components. 

We can find the horizontal velocity using the cosine function, initial velocity, and angle.

We can find the vertical velocity using the sine function, initial velocity, and angle.

The horizontal velocity is not going to change, since there is no horizontal acceleration. The vertical velocity, however, will be affected by gravity.

We know that the rock is going to travel a net displacement of , as that's the distance between the rock's initial position (the top of the building) and the ground. The displacement must be negative because the rock is traveling downward. Using the appropriate motion equation, we can use the rock's initial velocity, displacement, and acceleration to find the final velocity.

Keep in mind that square roots can be positive or negative. Since the rock is traveling in the downward direction, we need to take the negative root.

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We now have both the final horizontal and final vertical velocities. Use the Pythagorean Theorem to find the total velocity from the directional velocities.

To find the angle, we will need to find the final horizontal and vertical velocities. First, break our given velocity into its horizontal and vertical components. 

We can find the horizontal velocity using the cosine function, initial velocity, and angle.

We can find the vertical velocity using the sine function, initial velocity, and angle.

The horizontal velocity is not going to change, since there is no horizontal acceleration. The vertical velocity, however, will be affected by gravity.

We know that the rock is going to travel a net displacement of , as that's the distance between the rock's initial position (the top of the building) and the ground. The displacement must be negative because the rock is traveling downward. Using the appropriate motion equation, we can use the rock's initial velocity, displacement, and acceleration to find the final velocity.

Now that we have the final directional velocities, we can use the tangent function to find the angle with which the rock impacts the ground.

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