Projectile motion- only distance is known

In summary, the problem involves a baseball being thrown from shortstop position to first base, traveling 32m horizontally, rising 3mm and falling 3m. The goal is to find the velocity of the ball. The given equation, d=v(t)+0.5(a)(t)^2, is used to solve the problem. The initial height of the ball is unknown and the shortstop's height is most likely not 3m-3mm. Other relevant equations for projectile motion include v=d/t, v2^2=v1^2+2a(d), and the quadratic formula. The vertical component of the velocity can be found by using the equation
  • #1
sean-820
25
0

Homework Statement



A baseball, thrown from shortstop position to first base travels 32m horizontally, rises 3mm and falls 3m. Find the velocity of the ball.

Homework Equations



d=v(t)+0.5(a)(t)^2



The Attempt at a Solution



So i know horizontal motion will be a constant velocity and vertical will have acceleration
(-9.8m/s/s)

For the equation i know d=2.997m, a=-9.8m/s/s but there are still two unknowns. I was thinking of substitution or elimination to get rid of a variable, with anything i sub in has a variable so it gets no where.

If there was one more given it would be easy, but i can't get anywhere with just displacement other then the time it takes just to drop it (which should be the time when its dropped 3mm to the ground but i don't know that smaller distance.

Gan somebody help me with what my next step should be?
 
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  • #2
Your problem is not that you don't have enough givens' it is that you have not listed enough relevant equations. What other equations do you know about projectile motion?

Are you sure that the ball rises 3 mm and falls 3 m? Try to picture this. If the ball falls an overall distance of 2.997 m, from what height was it launched? How tall is a shortstop?
 
  • #3
kuruman said:
Your problem is not that you don't have enough givens' it is that you have not listed enough relevant equations. What other equations do you know about projectile motion?

Are you sure that the ball rises 3 mm and falls 3 m? Try to picture this. If the ball falls an overall distance of 2.997 m, from what height was it launched? How tall is a shortstop?

Would the shortstop not be 3m-3mm tall?

Other formulas:
v=d/t
v2^2=v1^2+2a(d)
quadratic formula- (-b+- sqrt(b^2-4ac))/2a
but i don't have enough info to sub in.
I looked in my notes and textbook and the formula i gave is the one we are using. i didnt see any other formulas other then kinematics formulas like the ones i gave above.

I don't even know the angle it is launched at other then the projectiles peak



The exact question is A baeball thrown from shortstopposition to first base, travels horizontally 32m, rises 3mm and falls 3m. Find the initial velocity. 3mm does sound like it could be a typo as its a small distance, but its what's in the question.
 
  • #4
sean-820 said:
Would the shortstop not be 3m-3mm tall?
Probably not. Three meters is about ten feet. Considering that shortstops release the ball from about shoulder height, this particular shortstop would have to be about twelve feet tall. The tallest person in the world, ever, is less than nine feet.

Be that as it may, since the silly numbers you are given are what you have to work with, you should be able to find the vertical component of the initial velocity using one of the equations that you have listed so far. How do you think you can do that?
 
  • #5
would mgh=0.5mv^2 work too I am assuming. Mass can cancel out. and i know gravity and height so the only variable would be vertical component. Now that you point it out it seems much easier as i was trying to find the horizontal component first.

The question isn't worded the best as it could also mean the ball hits the ground after 32m if the ball travels 32m per 3mm rise then in addition to that it falls

thanks for the help btw.
 
  • #6
sean-820 said:
would mgh=0.5mv^2 work too I am assuming.

That would work. I trust you can finish the problem now.
 
  • #7
I hope it's okay to post in this thread even though it's 1.5 years old, but which equation is kuruman referring to, that you can use in order to determine the vertical component of the velocity? Is it the quadratic formula?
 
  • #8
Use the same equations as for horizontal velocity, with the acceleration equal to g.
 
  • #9
But doesn't horizontal velocity have no acceleration, since the speed is constant? Which horizontal velocity equation has acceleration in it?
 
  • #10
Basic constant acceleration equations:
v=v_0+at
x=x_0+v_0t+(1/2)at^2
v^2=(v_0)^2+2aΔx
 

What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It follows a curved path and can be described using principles of physics, such as kinematics and dynamics.

What is the difference between distance and displacement in projectile motion?

Distance is the total length of the path traveled by an object, while displacement is the shortest distance between the initial and final position of the object. In projectile motion, the distance is known, but the displacement is unknown.

How do you calculate the time of flight in projectile motion?

The time of flight, or the time it takes for a projectile to reach its maximum height and return to its original height, can be calculated using the formula t = 2*v*sinθ/g, where v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

What factors affect the horizontal distance traveled in projectile motion?

The horizontal distance traveled in projectile motion is affected by the initial velocity, launch angle, and the acceleration due to gravity. Air resistance and wind can also have an impact on the horizontal distance.

How is projectile motion used in real life?

Projectile motion is commonly used in sports, such as basketball and baseball, where players need to calculate the trajectory of their shots. It is also used in engineering, such as in the design of bridges and buildings, to calculate the forces acting on structures. Projectile motion is also used in military applications, such as in the design of weapons and missiles.

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