Initial velocity of soccer ball and length of time in the air- projectile motion

[dani123]

Homework Statement

A soccer ball is kicked at 38.0° with respect to the horizontal and travels 64.0m before striking the ground.
a) what is its initial velocity?
b) how long was it in the air?

Homework Equations

d_v=1/2*at²
d_h=V_h*Δt
Kinetic equation d=V_i*t+ 1/2*at²
d_h=-V²*sin2θ /g
sinθ=opp/hyp
cosθ=adj/hyp
Δt=-2Vsinθ / g

The Attempt at a Solution

a) d_h=cos(38)*64m= 50.4m
d_v=sin(38)*64m=39.4m

Find t=√(39.4m/(0.5*9.8))=7.96s

plug this value into the d=V_i*t+ 1/2*at² equation and solve for V_i if d=64m

V_i=3.14m/s

b) V=d_h/Δt= 50.4m/7.96s=6.33m/s

Then solve for Δt=-2Vsinθ / g= 0.80s

I would like for someone to just double check my answers and that I used the appropriate equations and that the number of significant figures are being respected! Thanks so much in advance!

 

[BruceW]

I don't think you've done this one correctly. When the question says it travels 64m before striking the ground, I think it means this is the horizontal displacement.

Edit: as a hint d_h=V_h*Δt is the equation for the horizontal displacement, where you can use the horizontal component of initial velocity for V_h. And d=V_i*t+ 1/2*at² is the equation for vertical displacement, where you can use the vertical component of initial velocity for V_i. You will need to make use of both these equations simultaneously to solve the problem.

 

[dani123]

Thank you for your time but I am still so lost here.

 

[BruceW]

Maybe start with the equations that you need to use. The horizontal and vertical motion are separate, so there are 2 equations. Have you been through this kind of question in class?

 

[dani123]

Well this a correspondance course that I taking through the department of education so I am kind of teaching myself, which is making these assignments a bit more challenging but thankfully I have this forum to kind of guide me in the right direction.

I tried to redo this problem after consulting my textbook again and came up with the following:
For part a) I used d_h=-V²sin2/g, which lead me to getting V= 25.42m/s as my answer for this section.

For part b) Δt=Δx/V_x, and from this equation I got 2.52 seconds.

Are these answers correct? Thank you so much for your time and help.

 

[BruceW]

You've got part a) correct. But I get a different answer for part b), what did you use for Δx and V_x ?

 

[dani123]

I used Δx=64m and V_x=25.42m/s

 

[BruceW]

V_x is the component of velocity in the horizontal direction, not the total initial velocity. So you need to do a little trigonometry to get V_x from V. (as a check, V_x should come out as less than V, so it will be less than 25.42m/s).

 

[dani123]

Ok so I did a little trigonometry and got the velocity in the horizontal direction to be equal to 20.03m/s... So with that, I plugged it back into my delta t equation to get 3.195 or 3.20 seconds. Does this seem correct? Thanks!

 

[BruceW]

Yep, that is all correct. Nice work! One other thing: I think you should only use 2 significant figures, in the answer, since you used 2 sig. fig. in the inputs of the equation (i.e. g=9.8 which is 2 sig. fig.)