A baseball is thrown with an initial velocity of 37 m/s at an angle of 26 degrees above horizontal, from the top of the building which is 72 meters high.
A. What will be the horizontal and vertical components of this baseballs velocity?
B. what will be the vertical velocity of this baseball at the highest point of its trajectory?
C. What will be the horizontal velocity for this baseball at the highest point of its trajectory?
D. What is the "trajectory"?
E. how long will it take this baseball to reach its highest point?
F. What will be the highest point reached by this baseball?
G. How long will it take this baseball to reach the ground?
H. How far from the base of the building will this baseball strike the ground?
You need to use vectors because there is an angle and you know the initial velocity, and acceleration but not the final velocity. Make a picture and write out all information given to you in columns labeled X and Y directions. Then plug them into different kinematic equations and try to find the answers. These are not plug and chug problems, you have to think about them and manipulate different equations to get the correct answers.
To answer these questions, we will use the equations of motion and some basic principles of physics. Let's go through each question one by one.
A. To determine the horizontal and vertical components of the baseball's velocity, we can use some trigonometry. The horizontal component (Vx) of the velocity is given by Vx = V * cos(θ), where V is the magnitude of the initial velocity (37 m/s) and θ is the angle above the horizontal (26 degrees). Therefore, Vx = 37 m/s * cos(26°). Calculate the value to find the horizontal component of the velocity.
For the vertical component (Vy), we use Vy = V * sin(θ). Substitute the values to find Vy.
B. The vertical velocity at the highest point of the trajectory, also known as the peak or apex, is zero. This occurs because the object changes direction at the highest point, and for a brief moment, it pauses before falling back down. So, the vertical velocity at the highest point is 0 m/s.
C. The horizontal velocity remains constant throughout the trajectory, as there is no force acting horizontally to change its value. Therefore, the horizontal velocity at the highest point will be the same as the horizontal component of the initial velocity, which we calculated in part A.
D. The "trajectory" refers to the path followed by an object in motion. In this case, the trajectory refers to the path followed by the baseball as it is thrown from the top of the building and falls back to the ground.
E. To find the time taken for the baseball to reach its highest point, we can use the equation for the vertical component of displacement under constant acceleration. The equation is: Δy = Vyi * t + (0.5) * a * t^2, where Δy is the displacement (72 m), Vyi is the initial vertical velocity (which we calculated in part A), t is the time, and a is the acceleration (-9.8 m/s^2). Rearrange the equation to solve for t and substitute the known values to find the time taken.
F. The highest point reached by the baseball will occur when the vertical velocity reaches zero before it starts falling back down. Therefore, the highest point reached by the baseball will be the displacement above the starting point. From the given information, we know that the building is 72 meters high. So, the highest point reached by the baseball will also be 72 meters.
G. The time taken for the baseball to reach the ground is equal to twice the time taken to reach the highest point. This is because the time taken to rise to the highest point is the same as the time taken to fall from the highest point to the ground. Multiply the time calculated in part E by 2 to find the total time for the baseball to reach the ground.
H. To find the horizontal distance traveled by the baseball, we can use the equation: Δx = Vx * t, where Δx is the horizontal displacement, Vx is the horizontal component of the velocity (calculated in part A), and t is the time taken to reach the ground (calculated in part G). Substitute the known values to find the horizontal distance traveled by the baseball.