What is the maximum height of a spring toy launched at an angle?

[Evangeline101]

Homework Statement

A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy?

Homework Equations

Δ[/B]d_v = v₁Δt + 1/2aΔt²

The Attempt at a Solution

[/B]
Calculate time:

Δt = 2.3 m/s / 9.8m/s²

= 0.23 s

Now calculate vertical motion:
Δd_v = v₁Δt + 1/2aΔt² *for vertical motion, let (up) be positive

Δd_v = (2.3 m/s) x (0.23s) + 1/2 (-9.8 m/s²) x (0.23s)²

Δd_v = 0.27 m [up]

The maximum height reached by the spring toy is 0.27 m [up].

Is this correct? I have a feeling I did it wrong because I did not use the angle they provided and only used the velocity.

 

[SteamKing]

Homework Statement

A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy?

Homework Equations

Δ[/B]d_v = v₁Δt + 1/2aΔt²

The Attempt at a Solution

[/B]
Calculate time:

Δt = 2.3 m/s / 9.8m/s²

= 0.23 s

Now calculate vertical motion:
Δd_v = v₁Δt + 1/2aΔt² *for vertical motion, let (up) be positive

Δd_v = (2.3 m/s) x (0.23s) + 1/2 (-9.8 m/s²) x (0.23s)²

Δd_v = 0.27 m [up]

The maximum height reached by the spring toy is 0.27 m [up].

Is this correct? I have a feeling I did it wrong because I did not use the angle they provided and only used the velocity.

No, it's not correct. Why didn't you calculate the vertical component of the initial velocity?

 

[Evangeline101]

No, it's not correct. Why didn't you calculate the vertical component of the initial velocity?

Okay, so I did it again with the vertical component of initial velocity.

Calculate vertical component of initial velocity:

V_1v = v₁sinθ

V_1v = (2.3 m/s) sin 78°

V_1v = 2.25 m/s [up]

Calculate time:

Δt = 2.3 m/s / 9.8m/s²

= 0.23 s

Calculate vertical motion:
Δdv = v1Δt + 1/2aΔt2 *for vertical motion, let (up) be positive

Δdv = (2.25 m/s) x (0.23s) + 1/2 (-9.8 m/s²) x (0.23s)²

Δdv = 0.26 m [up]

The maximum height reached by the spring toy is 0.26 m [up].

Is this better?

 

[SteamKing]

Okay, so I did it again with the vertical component of initial velocity.

Calculate vertical component of initial velocity:

V_1v = v₁sinθ

V_1v = (2.3 m/s) sin 78°

V_1v = 2.25 m/s [up]

Calculate time:

Δt = 2.3 m/s / 9.8m/s²

= 0.23 s

Calculate vertical motion:
Δdv = v1Δt + 1/2aΔt2 *for vertical motion, let (up) be positive

Δdv = (2.25 m/s) x (0.23s) + 1/2 (-9.8 m/s²) x (0.23s)²

Δdv = 0.26 m [up]

The maximum height reached by the spring toy is 0.26 m [up].

Is this better?

Much better.

 

[Evangeline101]

Much better.

Thanks for the help :)