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Stuck on M1 Question, Please Help!!!

I got stuck with this question, I tried to work it out but I get really bizzare answers that don't comply with the answer in the back of the textbook.

The question is: (I am only stuck on part B)

A pebble is projected vertically upwards with speed 21m/s from a point 32m above the ground

a) Find the speed with which the pebble strikes the ground
<---- Got this

B )Find the total time for which the pebble is more than 40m above the ground

I worked out the time taken for the ascent part of the jouney, and the time taken for the descent and added them together. Then I planned to find out the time it takes for the pebble to reach 8m above 32m and the time the pebble is below 40m on the other side (descent) and subtract these two times away from the total of the time taken for the ascent and descent. This is where I started to goet bizzare answers and SUVAT just messed up.

The answer to B is apparently 3.4s, but I don't want the answer I want to know the steps to get to the answer. Thanks!!!
Just find t at s = 8. You'll end up with a quadratic and when you have both answers just subtract the smallest from the largest.

So:

S = ut + 0.5at^(2)

8 = 21t-4.9t^(2)

4.9t221t+8=04.9t^{2}-21t+8=0
(edited 12 years ago)
Original post by ERdoctor
I got stuck with this question, I tried to work it out but I get really bizzare answers that don't comply with the answer in the back of the textbook.

The question is: (I am only stuck on part B)

A pebble is projected vertically upwards with speed 21m/s from a point 32m above the ground

a) Find the speed with which the pebble strikes the ground
<---- Got this

B )Find the total time for which the pebble is more than 40m above the ground

I worked out the time taken for the ascent part of the jouney, and the time taken for the descent and added them together. Then I planned to find out the time it takes for the pebble to reach 8m above 32m and the time the pebble is below 40m on the other side (descent) and subtract these two times away from the total of the time taken for the ascent and descent. This is where I started to goet bizzare answers and SUVAT just messed up.

The answer to B is apparently 3.4s, but I don't want the answer I want to know the steps to get to the answer. Thanks!!!



you are making this much too complicated.
Take upwards as positive
you have
u = 21
a = -9.8
s = 40 - 32 = 8
t = ?

use s = ut + 0.5at^2

solve the quadratic in t to find the 2 times at which the pebble is at the desired altitude.

subtract the answers to find the time it is above said altitude.
Can I ask why did you use 8 instead of 40?
Original post by H.C. Chinaski
you are making this much too complicated.
Take upwards as positive
you have
u = 21
a = -9.8
s = 40 - 32 = 8
t = ?

use s = ut + 0.5at^2

solve the quadratic in t to find the 2 times at which the pebble is at the desired altitude.

subtract the answers to find the time it is above said altitude.


Can I ask why did you use 8 instead of 40?
Original post by Yousef Khashaba
Can I ask why did you use 8 instead of 40?


s is measured from the starting place.

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