Projectile Motion Problem: Tennis Ball Clearance Calculation

In summary, to find the speed of the ball when it left the racquet, you need to use the equations of motion for both the x and y directions. The initial velocity in the y direction can be found by multiplying the total velocity by the sine of the angle of 3 degrees. The initial velocity in the x direction can be found by multiplying the total velocity by the cosine of the angle of 3 degrees. Once you have both initial velocities, you can use them to solve for the time in both directions using the equation s=v0t+(1/2)at^2. Finally, you can use the time to eliminate it from the equation and solve for the total velocity of the ball.
  • #1
m_scott
10
0

Homework Statement


A tennis player standing 12.6m from the net hits the ball at 3 degrees above the horizontal. To clear the net, the ball must rise at least .330m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racquet?


Homework Equations


I tried using v2=v02+2a(x-x0)


The Attempt at a Solution


I have no clue
 
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  • #2
welcome to pf!

hi m_scott! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)

you need two equations, one for the x and one for the y direction …

then eliminate t …

what do you get? :smile:
 
  • #3
I still don't completely understand. What formulas am i supposed to use? And I am not sure what to do with the .330m

I set it up as: 0(final velocity)= v02+2(-9.8)(12.6) and got 15.7 but i know that's wrong...
 
  • #4
Hi m_scott.
You must see the motion of the ball as a composition of two kinds of motion: one in the horinzontal axis and another in the vertical axis.
Which kind of motion on the x axis?
Which kind of motion on the y axis?
Try to write the equations of motion for each axis.
And from it, up to you...
 
  • #5
uhh? :redface: forget the final velocity …

nobody asked for it! :wink:
 
  • #6
what equation should i use to find motion for the x and y axis?
 
  • #7
What kind of motion do you think that has the ball on the y direction ?
 
  • #8
well, you're only given s and vi and a (a = 0 for the x direction, = -g for the y direction), and you want to find t for both directions and then eliminate it …

so which of the standard constant acceleration equations do you think you should use? :smile:
 
  • #9
s=v0t+(1/2)at2??

And if so, do i plug in -9.8 for a and 0 for v0?

i got 1.6s Is that for the x or y axis?
 
  • #10
m_scott said:
s=v0t+(1/2)at2??

yes :smile:
And if so, do i plug in … 0 for v0?

no, v0 will be the initial component of velocity in the y direction
 
  • #11
Ok. How do I find the initial component of velocity in the y direction? Btw, sorry for all the newb questions. This is my 3rd day in physics and I am kinda lost...
 
  • #12
total velocity times sin3°

(and the initial x component is total velocity times cos3°)

haven't you done components? :confused:
 
  • #13
But the problem doesn't give me the total velocity
 
  • #14
that's right, it asks you for the total velocity …

so call that v, and solve :wink:
 

What is projectile motion?

Projectile motion is the motion of an object through the air under the force of gravity, with no other forces acting on it.

What are the key components of a projectile motion problem?

The key components of a projectile motion problem are the initial velocity, the angle at which the object is launched, the acceleration due to gravity, and the time it takes for the object to reach its maximum height or hit the ground.

How do you calculate the range of a projectile?

The range of a projectile can be calculated using the formula R = v02 * sin(2θ)/g, where R is the range, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

What is the maximum height of a projectile?

The maximum height of a projectile can be calculated using the formula h = (v02 * sin2(θ))/2g, where h is the maximum height, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

How does air resistance affect projectile motion?

Air resistance can affect the range and trajectory of a projectile, as it creates a force in the opposite direction of the object's motion. This can cause the object to slow down and fall at a steeper angle, resulting in a shorter range and lower maximum height.

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