Baseball projectile motion question

In summary, a ball player hits a home run with a baseball that just clears a wall 8.00 m high, located 104.8 m from home plate. The ball is hit at an angle of 38.4 degrees to the horizontal, with negligible air resistance. The acceleration of gravity is 9.81 m/s^2. Using the SUVAT equations and compensating for the initial height of 1.2 m, it is determined that the initial speed of the ball is 112 m/s (a), it takes 1.18 seconds for the ball to reach the wall (b), and the speed of the ball when it reaches the wall is approximately 105 m/s (c).
  • #1
jj8890
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0
[SOLVED] Baseball projectile motion question

Homework Statement


A ball player hits a home run, and the baseball just clears a wall 8.00 m high located 104.8 m from home plate. The ball is hit at an angle of 38.4 degrees to the horizontal, and air resistance is negligible. Assume the ball is hit at a height of 1.2 m above the ground. The acceleration of gravity is 9.81 m/s^2.
a) What is the initial speed of the ball?
b) How much time does it take for the ball to reach the wall?
c.) Find the speed of the ball when it reaches the wall.

Homework Equations


x(t)-Vo cos(theta)t
y(t)= -.5gt^2 +Vosin(theta)t+yo
V^2 = Vo^2 - 2 g (y - y°)

The Attempt at a Solution


Ok this is what I did...
Let X axis horizontal, and Y axis vertical upward. The equations of the ball are:
x(t) = Vo cos38.4° t
y(t) = - (1/2) g t^2 + Vo sin38.4° t + yo.
When x(t) = 104.8 m , y(t) = 8 m.
Solving : Vo = 33.9 m/s (a) ; t = 3.94 s (b)
(c) Energy's conservation
V^2 = Vo^2 - 2 g (y - y°)
V = 31.88 m/s (c)

I'm not sure if this is right though. I would appreciate any help. I think you may have to compensate for the 1.2 m high starting position.
 
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  • #2
Show your steps

For part A. How did you get around your unknown: time?
 
  • #3
Well, I have changed what I think it is since i posted.I tried using the SUVAT equations and I actually compensated for the 1.2 m initial height. See work below:
Horizontal: s=104.8, v=u=Ucos(38.4), t=?
Vertical: s=6.8, a=-9.81, u=Usin(38.4), t=?, v=0
s=vt-0.5a(t^2) (one of the "suvat" equations)
6.8/4.905=t^2
t=1.18s (3sf) (answer b)

back to horizontal...
Ucos(38.4)=s/t=104/1.18 (speed=distance/time)
U=104/1.18cos(38.4)
U=112 m(s^-1) (answer a)

v=112cos(38.4)
v=87.8 m(s^-1)

back to vertical: v=u+at=112sin(38.4)-9.81x1.18 (another suvat equation)
v=58.0 m(s^-1)

overall velocity= [58^2+87.8^2]^0.5 (pythagoras)
=105 m(s^-1) (answer c)
 
  • #4
Does the above look right?
 
  • #5
Can anyone help me with this?
 

Related to Baseball projectile motion question

1. What is projectile motion in baseball?

Projectile motion in baseball refers to the curved path that a baseball takes when thrown or hit. It is a combination of horizontal and vertical motion, influenced by factors such as gravity, air resistance, and the initial velocity of the ball.

2. How does the angle of release affect the trajectory of a baseball?

The angle of release, or the angle at which the ball is thrown or hit, plays a significant role in the trajectory of a baseball. A lower angle will result in a flatter, more horizontal trajectory, while a higher angle will create a steeper, more curved path.

3. What is the relationship between velocity and distance in baseball projectile motion?

The velocity of a baseball is directly related to the distance it will travel. The greater the initial velocity, the farther the ball will go. However, as the ball travels, air resistance will slow it down, so the distance will also depend on the launch angle and other factors.

4. How does air resistance affect the flight of a baseball?

Air resistance, or drag, is a force that opposes the motion of a baseball through the air. As the ball moves, it creates friction with the air, slowing it down and altering its trajectory. The amount of air resistance depends on the speed, size, and shape of the ball.

5. Can you predict the trajectory of a baseball using mathematical equations?

Yes, the trajectory of a baseball can be predicted using mathematical equations, such as the kinematic equations of motion. These equations take into account factors such as initial velocity, launch angle, and air resistance to calculate the position and velocity of the ball at any given time during its flight.

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