We first need to find the horizontal component of the initial velocity.

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

The only force acting on the rock during flight is gravity; there are no forces in the horizontal direction, meaning that the horizontal velocity will remain constant. We can set up a simple equation to find the relationship between distance traveled and the velocity.

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

We need to solve for the time that the rock travels upward. We can then add the upward travel time to the downward travel time to find the total time in the air.

Remember that the vertical velocity at the highest point of a parabola is zero. We can use that to find the time for the rock to travel upward.

Now let's find the time for the downward travel. We don't know the final velocity for the rock, but we CAN use the information we have been given to find the height it travels upward.

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

This means that our  will be  as it will be traveling down from the highest point. Using this distance, we can find the downward travel time.

Add together the time for upward travel and downward travel to find the total flight time.

Now that we've finally found our time, we can plug that back into the equation from the beginning of the problem, along with our horizontal velocity, to solve for the final distance.

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

To find the horizontal velocity we use the equation .

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

We can find the vertical velocity using the equation .

The horizontal velocity will not change during flight because there are no forces in the horizontal direction. The vertical velocity, however, will be affected. We need to solve for the final vertical velocity, then combine the vertical and horizontal vectors to find the total final velocity.

We know that the rock is going to travel a net distance of , as that is the distance between where the rock's initial and final positions. We now know the displacement, initial velocity, and acceleration, which will allow us to solve for the final velocity.

Because the rock is traveling downward, our velocity will be negative: .

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

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

To find the horizontal velocity we use the equation .

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

We can find the vertical velocity using the equation .

The horizontal velocity will not change during flight because there are no forces in the horizontal direction. The vertical velocity, however, will be affected. We need to solve for the final vertical velocity, then combine the vertical and horizontal vectors to find the total final velocity.

We know that the rock is going to travel a net distance of , as that is the distance between where the rock's initial and final positions. We now know the displacement, initial velocity, and acceleration, which will allow us to solve for the final velocity.

Because the rock is traveling downward, our velocity will be negative: .

Now that we know our final velocities in both the horizontal and vertical directions, we can find the angle created between the two trajectories. The horizontal and vertical velocities can be compared using trigonometry.

,

Plug in our values and solve for the angle.

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

To find the horizontal velocity we use the equation .

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

We can find the vertical velocity using the equation .

The question asks for the total velocity at the maximum height. At the top of the parabola, as the direction of the motion changes from upward to downward. Yet, even though it has no vertical velocity, the horizontal velocity remains constant during flight. The only force on the rock is that of gravity, and gravity will only affect the vertical velocity. There are no horizontal forces present to alter the horizontal velocity.

Our final answer will be equal to the horizontal velocity: .

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.

.

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.