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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