The speed which a ball must be thrown to reach 8m.

[Meezus]

Homework Statement

An object of mass 0.2 kg is thrown vertically upwards from ground level and reaches a height of 8.0 m. Calculate: the speed with which it must be thrown.

Homework Equations

Vf² – Vo² = 2gH

The Attempt at a Solution

Vf² – Vo² = 2gH
Vf = Final Velocity = 0 (Ball at maximum height)
Vo = Initial Velocity.
g = 9.8
H =8m
0 - Vo2 = 2 x -9.8 x 8 = -156.8

This is my attempt so far but I'm getting a negative answer, can anyone show me where I'm going wrong?

 

[Hesch]

Suggesting there is no air resistance ( no loss of energy ):

½*m*V₀² = m*g*H →

V₀² = 2*g*H

or you could say:

V₀² – V_f² = 2*g*H ( V_f = 0 ).

 

[Meezus]

Suggesting there is no air resistance ( no loss of energy ):

½*m*V₀² = m*g*H →

V₀² = 2*g*H

or you could say:

V₀² – V_f² = 2*g*H ( V_f = 0 ).

This is what I'm already doing but getting a negative number? Should I just be times by 9.8 not -9.8?

 

[Hesch]

No, I have switched the order of velocities, V₀ and V_f .
This will change the sign of the result.

 

[Hesch]

And you should use g = +9.8 m/s².
Otherwise the potential energy will be negative.

 

[Meezus]

And you should use g = +9.8.
Otherwise the potential energy will be negative.

so V0² – Vf² = 2*g*H ( Vf = 0 ).
0 - Vf² = 2 x 9.8 x 8 = 156.8.

is this correct?

 

[Hesch]

No, your first line is correct, but the second is not.

V₀² is not equal to 0.

 

[Meezus]

No, your first line is correct, but the second is not.

V₀² is not equal to 0.

V0² = 2*g*H

so V0²= 2 x 9.8 x 8 = 156.8

 

[Hesch]

Yes.

Remember units!

 

[Meezus]

Yes.

Remember units!

156.8 m/s correct?
and thank you

 

[Hesch]

No, try to insert units in this calculation:

2 x 9.8 x 8 = 156.8

Will the unit of the result be m/s? Or will it be m²/s²?
Why?

 

[Hesch]

V₀² = 2 × 9.8 [m/s²] × 8 [m] = 156.8 [m²/s²] →
V₀ = √(156.8 [m²/s²]) = 12.52 [m/s]

Always check the units. Then you can see if something is wrong in your calculation.
Here the square root was missing.

 

[Meezus]

V₀² = 2 × 9.8 [m/s²] × 8 [m] = 156.8 [m²/s²] →
V₀ = √(156.8 [m²/s²]) = 12.52 [m/s]

Always check the units. Then you can see if something is wrong in your calculation.
Here the square root was missing.

Thank you for all your help :) it is greatly appreciated