Projectile motion long jumper help

[Amel]

Homework Statement

An Olympic long jumper is capable of jumping 7.7m. Assuming his horizontal speed is 8.8m/s as he leaves the ground, how long is he in the air? Assume that he lands standing upright--that is, the same way he left the ground.

Homework Equations

Y = xtan(theta)₀ - ((g)/2V₀²cos²(theta)₀)X²

V_x0 = V₀cos(theta)t

And other that I attempted at using...

The Attempt at a Solution

Ok so I have tried several things but, I don't have the angle at which he jumps to figure out the time, and you only get the initial velocity for the horizontal direction. I was going to use

V_x0 = V₀cos(theta)t

to solve for Cos(theta) and figure out my angle but I don't even Have V, only V_x so am I suposed to assume they are the same?

If someone can point me in the right direction, this is the only problem I couldn't figure out earlier today.

 

[Amel]

Also I can't remeber exactly all the work I did today my work is kind of unorganized and its all over the place but I came to the conclusion that t was 1.11 but that was wrong.

 

[drizzle]

V_x0 = V₀cos(theta)t

are you sure of this?, I don't think there's a "t" in that equation

 

[Amel]

Oh hold up I mixed up two equation when writing this they were next to each other on my paper.

I got V_x0=V₀cos(theta)

and X = V₀cos(theta)t

my bad.

 

[jacarecanga]

The only acceleration that the long jumper is subject to is the acceleration due to gravity then no acceleration acts to oppose the long jumpers horizontal motion. Therefore his horizontal velocity remains constant. This problem simply breaks down to d/v=t. 7.7m/(8.8m/s)=.875s

 

[Amel]

Wow so simple, I didn't even think about it like that I was trying to do it like the other projectile motion problems I did today. Thank you.

 

[Amel]

Alright quick question... Is V the same as V_x0 because there is acceleration in the y direction so there is a vetical velocity component right? Because I am trying to now figure out how hight he goes.

So I figure I use Y= V₀sin(theta)t- (1/2)gt² but I don't have an angle. Which I thoguth I could figure out with X = V₀cos(theta)t but I don't know V I only know V_x.

 

[drizzle]

no! that'll be true only if his motion was a straight one [as running]. does 7.7 m stands for the height y or the horizontal distance x? if the later, it'll be direct. use the last two equations you’ve stated in your later post to find t, that is:


V_x0=V₀cos(theta)

and

X = [V₀cos(theta)]t

 

[Amel]

7.7m is the distance he jumps in the X direction.

 

[drizzle]

great, what's t value?

 

[Amel]

The time the way he gave me was correct (we input our answers online, and it accepted it as correct) So I know the time, but how do I get the height without having an angle he jumps at, and I don't know how to get the angle without V since I only have V_x

 

[drizzle]

you have x,V_o and t, use the 2^nd eq. to get the angle

 

[jacarecanga]

The jumper will reach his maximum height at t/2. For a hint. If you need more help let me know.

 

[jacarecanga]

You only have V[0][x] not V[0]

 

[Amel]

So in this problem is V = V_x? If that's so then

X = [V0cos(theta)]t

Then the I would divide by t and V⁰ right? which gives me .9943 = cos(theta) so then inverse cos of .9943 would give me my angle? which I got to be 6.11 which doesent seem right, but I then used that and the Y I got was incorrect.

ok just saw the post that says you got Vx not V and then how do I find the angle without V?

 

[Amel]

I have two attempts left on the problem and I don't know how to find the angle. So I can't guess anymore, need some hints. I mean I know if you want to maximize your X you would jump at a angle of 45 but not sure if you can assume that here and don't want to waste my attempt trying it.

 

[Amel]

Ok on my last attempt, someone please help out before I screw it up. How can you find the angle if you don't know V₀?

 

[Amel]

Damn used up my last attempt and wasn't able to get the maximum height.

 

[drizzle]

type the eq. of V_y!

 

[rl.bhat]

The projectile equation is
Y = xtan(θ) - (g)x^2/2(V0^2cos^2(θ)
Τhe net displacement is zero. Hence
xtan(θ) = (g)x^2/2(V0^2cos^2(θ) or
tan(θ) - (g)x/2(V0^2cos^2(θ) or
tan(θ) = gx/2(vx)^2
Substitute the values and find θ.

 

[drizzle]

OR, using the 2nd eq. →V_o=V_xo/cos(theta)
you can substitute this into the Vy eq. which is
V_y= V_o sin(theta) – gt
you'll get
V_y= V_xo tan(theta) – gt
now you can calculate the value of theta, by lodging the value of (t/2) where at the maximum height the value of Vy is zero,


you should never give up hope Amel!

Amel means hope, right?