Solving for the Angle of a Baseball's Velocity in Projectile Motion

[lev1234]

Homework Statement

A 72 g autographed baseball slides off of a
1.3 m high table and strikes the floor a hori-
zontal distance of 0.7 m away from the table.
The acceleration of gravity is 9.81 m/s2 .

What was the direction of the ball’s velocity
just before it hit the floor?
That is, at what angle (in the range −90◦ to
+90◦ relative to the horizontal directed away
from the table) did the ball hit the floor?
Answer in units of degrees

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi lev1234! Welcome to PF!

The ball slides off the table, so its initial velocity is horizontal.

Treat movement in the x and y directions separately.

 

[kerimek]

I would first approach this problem by breaking it down into smaller components and using the principles of projectile motion to solve for the angle of the ball's velocity. I would start by identifying the known values, such as the mass of the ball (72 g), the height of the table (1.3 m), and the horizontal distance traveled (0.7 m). I would also take note of the acceleration of gravity (9.81 m/s2) as it will affect the ball's trajectory.

Next, I would use the equations of motion for projectile motion, such as the equation for horizontal displacement (x = v*cosθ*t) and vertical displacement (y = v*sinθ*t - 0.5*g*t^2). By plugging in the known values and solving for the time (t), I can then use the horizontal displacement equation to solve for the initial velocity (v) of the ball.

Once I have the initial velocity, I can use trigonometry to solve for the angle (θ) at which the ball hit the floor. This can be done by using the inverse tangent function (tan^-1) and plugging in the values for the horizontal and vertical components of the velocity. The resulting angle will be the direction of the ball's velocity just before it hit the floor.

In this particular scenario, the angle would be in the range of -90° to +90°, with negative angles indicating that the ball was moving downward and positive angles indicating that it was moving upward. The direction of the velocity would be away from the table, as stated in the question.

In conclusion, by using the principles of projectile motion and applying mathematical equations and trigonometry, I can determine the angle at which the baseball's velocity was directed just before it hit the floor. This information can be useful in understanding the trajectory and motion of objects in projectile motion.