What Is the Expression for Acceleration in This MCQ?

[O.J.]

hello,

i have this question that's buggin me :

two markers M1 and M2 are vertically h meters apart. a steel ball is released x m above M1 and reaches M1 by time t1 and M2 by time t2. what's the expression for acceleration?

a.) 2h/(t2)^2
b.) 2h/(t1+t2)
c.) 2h/(t2-t1)^2
d.) 2h/(t2^2-t1^2)

 

[Andrew Mason]

hello,

i have this question that's buggin me :

two markers M1 and M2 are vertically h meters apart. a steel ball is released x m above M1 and reaches M1 by time t1 and M2 by time t2. what's the expression for acceleration?

a.) 2h/(t2)^2
b.) 2h/(t1+t2)
c.) 2h/(t2-t1)^2
d.) 2h/(t2^2-t1^2)

You have to start with the equation for distance fallen. You should know that.

Write out the expression for the distance fallen in time t1 (= x). Write out the expression for the total distance fallen at time t2 (= x+h). Subtract the two equations to get the equation for the difference (h). Work out a from that (which, if it is on earth, is g).

AM

 

[O.J.]

i really am confused. can u show me how to work it out?

 

[pizzasky]

Reply

In this question, your ultimate goal is to find the acceleration.

As Andrew Mason mentioned, you need to "write out the expression for the distance fallen in time t1 (= x)". What variables are present? Do you know which Kinematics equation you should use?

Similarly, you will need to "write out the expression for the total distance fallen at time t2 (= x+h)". Use the appropriate Kinematics equation here as well.

Carry out some algebraic manipulation, and you should get the answer!

If you need more help, please show some of your working first.

Hint: The steel ball was released from rest.

All the best!

 

[O.J.]

ok, this is my workin,

the vertical distance between the M1 and M2 is h. initial velocity (u) at M1 is found by:

s=(v+u)/2 x t
x=(0+v)/s x t1

we get v=2x / t1, and this is = u for the 2nd part

similarly, v= (2x+2h)/t2

we can also get t as (t2-t1)

so we have v,u,s and t. we can use anythree of them in a kinematics equation to simplify an expression for a. but when I am doing it I am getting complicated expressions that don't simplify to any of the options

 

[Andrew Mason]

ok, this is my workin,

the vertical distance between the M1 and M2 is h. initial velocity (u) at M1 is found by:

s=(v+u)/2 x t
x=(0+v)/s x t1

we get v=2x / t1, and this is = u for the 2nd part

similarly, v= (2x+2h)/t2

we can also get t as (t2-t1)

so we have v,u,s and t. we can use anythree of them in a kinematics equation to simplify an expression for a. but when I am doing it I am getting complicated expressions that don't simplify to any of the options

You can use $s = vt/2$ but since v = at, this works out to:

$$s = \frac{1}{2}at^2$$

so:
(1) $$x = \frac{1}{2}at_1^2$$ and

(2) $$x + h = \frac{1}{2}at_2^2$$

Subtracting (1) from (2):

$$h = \frac{1}{2}at_2^2 - \frac{1}{2}at_1^2$$

Rearrange the expression for a and you will have your answer.

AM

 

[O.J.]

thanks a lot