How Much Does a Baseball Drop When Thrown Horizontally at 46.8 m/s Over 15.7 m?

In summary, a major-league pitcher can throw a baseball at a speed of 46.8 m/s. If thrown horizontally, the ball will drop 15.98 meters by the time it reaches a catcher who is 15.7 meters away. The equation used to determine this is x=x_0 + v_0*t - g/2*t^2, where x is the final distance, x_0 is the initial distance, v_0 is the initial velocity, t is time, and g is the acceleration due to gravity.
  • #1
triplel777
35
0

Homework Statement



A major-league pitcher can throw a baseball in excess of 46.8 m/s. If a ball is thrown horizontally at this speed, how much will it drop by the time it reaches the catcher who is 15.7 m away from the point of release?


Homework Equations





The Attempt at a Solution



i first found time using v=d/t
so 46.8 = 15.7/ t
t= 0.33

then i used the formula x=x_0 +v_0*t
so x=15.7+46.8*0.33
x= 31.14
 
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  • #2
You have the time, but you use the wrong distance formula. Remember that gravity is constantly accelerating the ball downwards.
 
  • #3
ok y=y_0 + v_0*t-g/2*t^2
y=0+46.8*0.33-g/2*t^2
y=15.98
 

Related to How Much Does a Baseball Drop When Thrown Horizontally at 46.8 m/s Over 15.7 m?

1. How does gravity affect a baseball when it is dropped?

When a baseball is dropped, it experiences a downward force due to gravity. This force causes the ball to accelerate towards the ground at a rate of 9.8 meters per second squared.

2. What is the relationship between the height from which a baseball is dropped and its speed when it hits the ground?

According to the principles of physics, the speed at which a baseball hits the ground when dropped from a certain height is directly proportional to the square root of that height. This means that as the height increases, the speed of the baseball also increases.

3. Does air resistance affect the speed of a baseball when dropped?

Yes, air resistance does affect the speed of a baseball when dropped. As the ball falls, it experiences air resistance, which is a force that opposes its motion. This force increases as the speed of the ball increases, eventually reaching a point where it balances out the force of gravity and the ball reaches a constant speed known as terminal velocity.

4. How does the mass of a baseball affect its acceleration when dropped?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. This means that a heavier baseball will experience a smaller acceleration due to gravity compared to a lighter baseball.

5. Can a baseball ever be dropped with a speed of zero?

No, according to the law of conservation of energy, the total mechanical energy of a system remains constant. When a baseball is dropped, its potential energy (due to its height) is converted into kinetic energy (due to its motion). This means that the baseball will always have a non-zero speed when it hits the ground.

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