What is the deceleration of the ball?

[Hussain]

Homework Statement

The question didn't fit there.
*A boy drops a metal ball from rest on sand. It hits the sand bed in one second and makes an impression of maximum depth 8mm in the sand. What is the average deceleration of the ball as it hits the sand? Assume air resistance is negligible.

vi= 0m/s
t= 1 sec
S= 8 mm or 0.008 m
a=?

Homework Equations

I used S=vit+1/2(at^2)

The Attempt at a Solution

By using that formula I got the answer 0.016 m/s^2 is it correct? Please tell me how to do it

 

[TomHart]

Welcome to Physics Forums.
You are using 1 second as the time, but that is the time the ball is falling - not the time that the ball is decelerated by the sand.

 

[Cepterus]

vi= 0m/s

This isn't correct: The ball is dropped from rest, but by the time it hits the sand, it already has a certain speed, as it is accelerated by gravity. So, what is $v_i$ when the ball reaches the ground?

 

[Hussain]

Welcome to Physics Forums.
You are using 1 second as the time, but that is the time the ball is falling - not the time that the ball is decelerated by the sand.

Which formula should I use now?

 

[TomHart]

The deceleration starts when the ball touches the sand. You need to know 3 things to solve. What is the velocity when the ball first touches the sand? What is the distance over which the deceleration occurs? What is the final velocity of the ball? You should use a formula which utilizes those 3 knowns and allows you to find the unknown (acceleration).

 

[haruspex]

The deceleration starts when the ball touches the sand. You need to know 3 things to solve. What is the velocity when the ball first touches the sand? What is the distance over which the deceleration occurs? What is the final velocity of the ball? You should use a formula which utilizes those 3 knowns and allows you to find the unknown (acceleration).

That is surely what the question intends, but the question is flawed. Average acceleration is Δv/Δt, so it would have to be possible to find the deceleration time. But there is not enough information in the question to find that.
We could find it by pretending the deceleration is constant from the instant of touching the sand to that of coming to rest, but that is clearly not the case, and the question would not need to ask for average deceleration.
A better wording would be "what is the deceleration as it presses into the sand, pretending it is constant?"