How long is discus in the air and the horizontal distance traveled

[dani123]

Homework Statement

A discus is released at an angle of 42.0° with respect to the horizontal and a velocity of 28.0m/s.

a)How long does it stay in the air?

b)What horizontal distance does it travel?

Homework Equations

dv=1/2*at²
dh=Vh*Δt
Kinetic equation d=V_i*t+ 1/2*at²
dh=-V²*sin2θ /g
sinθ=opp/hyp
cosθ=adj/hyp
Δt=-2Vsinθ / g

The Attempt at a Solution

hyp=28.0m/s

cos(42°)*28.0m/s=Vh= 20.8m/s
sin(42°)*28.0m/s=Vv= 18.7m/s

a) I used Δt=-2Vsinθ / g and solved for Δt=3.82s

b) Used dh=-V²*sin2θ /g to solve for dh= 79.6m

For part b) I don't know when you I am supposed to use dh=-V²*sin2θ /g equation and when I should just use dh=Vh*Δt or the d=V_i*t+ 1/2*at² equation. If anyone could give me any tricks or explanations of when and why we use that specific equation that would be greatly appreciated. Thank you so much in advance!

 

[tiny-tim]

hi dani123!

a)How long does it stay in the air?

b)What horizontal distance does it travel?
…
For part b) I don't know when you I am supposed to use dh=-V²*sin2θ /g equation and when I should just use dh=Vh*Δt or the d=V_i*t+ 1/2*at² equation.

(what's the dh=-V²*sin2θ /g equation? )

if you can use dh=Vh*Δt or d=V_i*t+ 1/2*at² then you certainly should

 

[dani123]

dh=-V2*sin2θ /g equation was given in my course book for finding the horizontal range of a projectile, launched at an angle.
Where V is the instantaneous projectile velocity,
θ is the angle of projection, and
g is the acceleration due to gravity which is equal to -9.80 m/s²
This equation can be used to find the horizontal range of projectile that returns to the same level from which it was launched (d_v=0), provided that angle of projection, θ, and the instantaneous projectile velocity, V, are known.

 

[tiny-tim]

ahh!

in that case, the answer to your original question …

For part b) I don't know when you I am supposed to use dh=-V²*sin2θ /g equation and when I should just use dh=Vh*Δt or the d=V_i*t+ 1/2*at² equation.

… is that both methods work, so you should use the quick method if you can remember it

(which I'm pretty sure you won't be able to in the exam )

 

[dani123]

Thank you!