Finding Acceleration Due To Gravity

[Dave Johnson]

Homework Statement

A Gak it a type of alien that lives on a planet in another galaxy. One day a Gak decides to find out a little more about his planet. He drops a ball (it starts at rest) with a mass of 4.88 kg and notes that it takes 0.712 s to fall a distance of 4.04 m.

What is the acceleration due to gravity on the Gak’s planet?

Homework Equations

mgh = 0.5mv^2

The Attempt at a Solution

V = 4.04/0.712 = 5.67m/s
g = (0.5V^2)/h = [0.5(5.67)^2]/4.04 = 3.98ms^-2

However, answer is incorrect. Can someone kindly help me please?

 

[Chandra Prayaga]

Your method of getting v is wrong. It only gives you the average speed. The instantaneous speed of the ball is changing all the time, as it falls. You should be able to use a formula which does not involve the speed, but involves only the quantities for which the data is given.

 

[Dave Johnson]

I see... But i can't seem to find any formula without any given radius.

 

[Chandra Prayaga]

Sorry. What is the radius we are talking about here?

 

[Dave Johnson]

the formula for acceleration due to gravity is g = G*M/R^2. R is the radius

 

[Chandra Prayaga]

But the data for the radius and mass are not given. So how do you use that?

 

[Dave Johnson]

Yap that why i said its hard to solve this question without radius.

 

[Chandra Prayaga]

Can you think of a formula that connects the distance the ball drops to time?

 

[Dave Johnson]

d = vt + (1/2)at2?

 

[Chandra Prayaga]

What is v in your formula?

 

[Dave Johnson]

0

 

[Chandra Prayaga]

So now you can find g, right?

 

[Dave Johnson]

yap cheers