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

#### Meezus

1. 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.

2. Homework Equations

Vf2 – Vo2 = 2gH

3. 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?

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#### Hesch

Gold Member
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 – Vf2 = 2*g*H ( Vf = 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 – Vf2 = 2*g*H ( Vf = 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

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

#### Hesch

Gold Member
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

Gold Member
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

Gold Member
Yes.

Remember units!

#### Hesch

Gold Member
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

Gold Member
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

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

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