Solve for Time in Air: Baseball Hit Problem | 30 m/s at 30 deg | Window at 12m

[seraphimhouse]

Homework Statement

After you hit a baseball, it flies into a window across the street. The baseball leaves your bat at a distance 1m above the ground, and the window is 12 m above the ground. The ball leaves your bat with a velocity of 30 m/s at 30 degrees.

How long was the ball in the air? Note: if your solution contains two roots, explain the meaning of each.

Homework Equations

Y = Yo + Vot - 1/2gt^2

The Attempt at a Solution

With that formula in #2. Vo = 0 m/s so Y = -1/2gt The magnitude of that gives me 3.06 s, but that does not correspond to the answer in the back of the book

 

[BishopUser]

Your attempted solution is not very detailed. Think about the meaning of each variable in the equation. You assumed Vo to be zero, but you know that stands for the initial velocity, right? Initial velocity of the ball is obviously not 0. Also Yo stands for initial height.

 

[nlightner]

.

I would first clarify the assumptions and conditions of the problem. Is the baseball traveling in a vacuum or through air? Is there any air resistance? Are we considering the effects of gravity? These factors can greatly affect the time in air for the baseball.

Assuming that we are dealing with a simplified scenario of a baseball traveling through air with no air resistance, we can use the equation Y = Yo + Vot - 1/2gt^2 to solve for time in air. In this equation, Y represents the vertical displacement of the baseball, Yo represents the initial height of the baseball, Vo represents the initial velocity of the baseball, g represents the acceleration due to gravity, and t represents time.

To solve for time, we need to first determine the vertical displacement of the baseball. In this case, the baseball starts at a height of 1m and reaches a height of 12m at the window. Therefore, the vertical displacement is 12m - 1m = 11m.

Next, we need to determine the initial velocity of the baseball in the vertical direction. Since the baseball is hit at an angle of 30 degrees, we can use the component method to determine the vertical component of the initial velocity. The vertical component can be calculated as Vo*sin(30), which is approximately 15 m/s.

Plugging in the values in the equation, we get 11 = 1 + 15t - 1/2*9.8*t^2. Solving for t, we get two roots: t = 0.76s or t = 2.13s. These roots represent the time at which the baseball reaches the window (t = 2.13s) and the time at which the baseball is at its maximum height (t = 0.76s). Therefore, the time in air for the baseball is 2.13 seconds.

In conclusion, the time in air for the baseball is 2.13 seconds, considering the assumptions and conditions stated above. However, if we consider air resistance and other factors, the time in air may vary. It is important to clearly state the assumptions and conditions when solving a problem in order to get an accurate and meaningful solution.