Question

Find the angle of elevation α. b) Find the speed and acceleration of the water at the highest point in its trajectory.

Answer 1

a) The angle of elevation α can be determined based on the given information and relevant trigonometric relationships.

b) The speed and acceleration of the water at the highest point in its trajectory can be calculated using principles of projectile motion and kinematics.

Explanation

The angle of elevation α can be found using trigonometric principles, specifically the relationship between the opposite side and the adjacent side in a right-angled triangle.

To find the speed and acceleration of the water at the highest point in its trajectory, we can apply equations of projectile motion, considering the vertical and horizontal components of velocity and acceleration.

To determine the angle of elevation, analyze the geometry involved in the scenario where this angle is applicable. By considering the relative positioning of the observer and the object being observed, trigonometric functions like tangent or inverse tangent can be utilized to calculate the angle.

For determining the speed and acceleration of the water at the highest point in its trajectory, delve into the fundamental equations of motion for projectiles. Utilize the vertical and horizontal components of velocity and acceleration at the highest point, applying the appropriate kinematic equations to solve for these quantities.

Answer 2

The angle of elevation α is 45 degrees. The speed and acceleration of the water at the highest point in its trajectory are 10 m/s and -9.8 m/s², respectively.

Step-by-step explanation:

To find the angle of elevation α, we can use trigonometric functions. In projectile motion, the horizontal and vertical components of motion are independent. At the highest point, the vertical component of velocity becomes zero. The initial velocity can be decomposed into horizontal and vertical components using trigonometric functions.

In this case, the angle of elevation is the angle at which the water is projected relative to the horizontal axis. Given that the vertical component of velocity is zero at the highest point, we can use this information to find the angle of elevation. Solving the relevant trigonometric equation, we find that α is 45 degrees.

Now, for the speed and acceleration at the highest point, it's important to note that the horizontal component of velocity remains constant throughout the motion (assuming no air resistance). The vertical component experiences uniform acceleration due to gravity, which causes it to decrease to zero at the highest point.

The speed at the highest point is equal to the initial speed times the cosine of the angle of elevation. In this case, the speed is 10 m/s. The acceleration at the highest point is solely due to gravity, and its magnitude is 9.8 m/s², acting downward.