Projectile motion (the dreaded volleyball problem)

[boomer77]

Homework Statement

A regulation volleyball court is L = 18.0 m long and a regulation volleyball net is d = 2.43 m high. A volleyball player strikes the ball a height h = 1.81 m directly above the back line, and the ball's initial velocity makes an angle theta = 48° with respect to the ground

find:
a.) vi the ball must be hit at to barely make it over the net
b.)the maximum height reached by the ball in this case
c.)vi for the ball to be hit so it directly lands on the opponent's back sideline
d.) the maximum height for the ball in this case
e.)maximum vi for the ball to barely make it over the net and just barely land in bounds
(for the contact point in previous problems, what is the maximum vi)
f.)if you hit the ball at this maximum vi, what angle should you hit it at?

Homework Equations

d=vt for the x direction

free fall equations for the y direction

The Attempt at a Solution

~i know the answer to a is 9.73 m/s what will i do with this in part b?

~for b. i would like to know how to set up this problem
correct any errors for this question please

dx=9.0m
vx= ?
t=9.0/vcos48

dy= 0.62m because it it hit i.81m above the ground
viy= ?
a=-9.8 m/s^2

~part c is basically like part a but dx is 18.0m and i believe your dy is 2.43

~i think part d is like part b

and i haven't tried part e or f so help will be of great appreciation! thanks to anyone who replies!

 

[CompuChip]

free fall equations for the y direction

The Attempt at a Solution

[...]
~for b. i would like to know how to set up this problem
correct any errors for this question please

What is the general formula for height (vertical distance) for a freely falling object (and watch the initial values, at t = 0).
At what time does it reach the highest point (what happens to the vertical velocity?).

 

[NinjaHelper]

The best way to do these problems is create a chart. Then from the chart, use some basic ideas and then apply the three basic equations for kinematics.

The way you setup the chart should look like this, where o (naught) means initial. Such as x_o means initial position along the x-axis.

http://students.washington.edu/angelofg/pictures/chart.jpg

Things to remember: there is usually no acceleration in the x-direction, and in the y-direction will usually be gravity. Time will be the same for both.

On a side note as well, the initial velocity will be the same for both. However, it will be a component. Since we've broke the vector up into x and y components we have V*cos(theta), and V*sin(theta) =). I will leave you to figure out which one goes to which.

The three equations are:
v = vo + at, x = xo + vot + (at^2)/2, and v^2 = vo^2 + 2*a*(x - xo). From here on, it's just algebra.

 

[boomer77]

~for part a the question was "at which initial speed must the player hit the ball so that it just barely makes it over the net?"

my work is as follows:

dx= 9.0
vx= vcos48=> .669
t= 9/v(.669)

dy=0.62m taking into account the height in which it was hit at
viy= vsin48=> .743
a=-9.8

d=vit+1/2at^2
.62= .669(12.11)-4.9(12.11/v)^2
-7.48=-718.6/v^2
v^2=96.06
v=9.73
my answer was correct

~for part b the question states "what is the maximum height above the court reached by the ball in this case?"

my work looked like this:

dx=9.0
vx= 9.73(.669)=> 6.51
t= 1.38

dy=?
viy= 9.73(.743)=> 7.23
vf=0
a=-9.8

vf^2=vi^2+2ad
0^2= 7.23^2+2(-9.8)(d)
-52.27= -19.6(d)
d= 2.66

i put this answer into my problem set and i also added this to the height of the net and it says my answer is wrong

~part c asks "at what initial speed mut the ball be hit so that it lands directly on the opponent's back line?"

i went about the problem just like part a but changed my dx to 18.0m and my dy to 2.43m giving me an answer of 14.44 and my problem set says it is wrong

could you explain why these answers are wrong?

 

[Doc Al]

~for part b the question states "what is the maximum height above the court reached by the ball in this case?"

my work looked like this:

dx=9.0
vx= 9.73(.669)=> 6.51
t= 1.38

Here you found the time to reach the net, which is not needed.

dy=?
viy= 9.73(.743)=> 7.23
vf=0
a=-9.8

vf^2=vi^2+2ad
0^2= 7.23^2+2(-9.8)(d)
-52.27= -19.6(d)
d= 2.66

This looks OK.

i put this answer into my problem set and i also added this to the height of the net and it says my answer is wrong

Why add the height of the net? Add the initial height of the ball.

~part c asks "at what initial speed mut the ball be hit so that it lands directly on the opponent's back line?"

i went about the problem just like part a but changed my dx to 18.0m and my dy to 2.43m giving me an answer of 14.44 and my problem set says it is wrong

I don't know anything about volleyball, but I assume the back sideline is at the other end of the court. Again, you used the height of the net instead of the initial height of the ball.

 

[boomer77]

ok so for part b my answer is now 4.47

for part c my problem should look like this

 

[boomer77]

dx=18
vx=vcos48
t=26.9

dy=0
viy=vsin48
a=-9.8
then use d=vit+1/2at^2?

 

[boomer77]

i mean dy=1.81 (whoops

 

[Doc Al]

dx=18
vx=vcos48
t=26.9

You mean: t = 26.9/v

dy=0
viy=vsin48
a=-9.8
then use d=vit+1/2at^2?

Yes, except that dy ≠ 0.

 

[boomer77]

that dy = 1.81 or is it negative?

 

[Doc Al]

that dy = 1.81 or is it negative?

It's negative.

 

[boomer77]

so here's my new work:

d=vit+1/2at^2
1.81= vsin48(26.9/v)-4.9(26.9/v)^2
1.81=19.99-(3545.7/v^2)
-18.1=-3545.7/v^2
v^2=195.9
v=13.99

my problem set is saying this answer is wrong, is there a flaw in my math?

 

[boomer77]

wait nevermind i didn't make that negative

 

[boomer77]

this is my new work

-1.81=vsin48(26.9/v)-4.9(26.9/v)^2
-1.81=19.9-(3545.7/v^2)
-21.8=-3545.7/v^2

 

[boomer77]

v^2=162.64
v=12.75

 

[boomer77]

ok so for part d i have to find the maximum height the ball will reach in this case so my work will be:

vf^2=vi^2+2ad
0=12.75^2+2(-9.8)d
-162.6=-19.6d
divided by -19.6
d=8.29
8.29+1.81
d=10.01

 

[boomer77]

...but it is wrong, and i don't know why

 

[Doc Al]

ok so for part d i have to find the maximum height the ball will reach in this case so my work will be:

vf^2=vi^2+2ad
0=12.75^2+2(-9.8)d
-162.6=-19.6d
divided by -19.6
d=8.29
8.29+1.81
d=10.01

Use the vertical component of the velocity.