A well has 15 steps inside it . The water level is at ninth step. A frog is sitting on the topmost step that is the first step.The frog jumps 3 step down and then jumps 2 step up . In how many jumps will it reach the water level ? after reching the water level the frog jumps 4 steps up and then 2 steps down in every move.In how many jumps will it return to the topmost step ?
Answers
Answer:
Step-by-step explanation:
Our question is: A well has 15 steps inside it . The water level is at ninth step. A frog is sitting on the topmost step that is the first step.The frog jumps 3 step down and then jumps 2 step up . In how many jumps will it reach the water level ? after reching the water level the frog jumps 4 steps up and then 2 steps down in every move.In how many jumps will it return to the topmost step ?
Since our aim is to know how many jumps will it return to the topmost step, we need to consider some steps to reach the final answer.
A well has 15 steps inside it . The water level is at ninth step. A frog is sitting on the topmost step that is the first step.The frog jumps 3 step down and then jumps 2 step up . In how many jumps will it reach the water level ? after reaching the water level the frog jumps 4 steps up and then 2 steps down in every move.In how many jumps will it return to the topmost step ?
1) the frog reaches the water level, the 9th step after 40 jumps.
2) The frog returns to the top after 24 jumps
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Answer:
A well has 15 steps inside it . The water level is at ninth step. A frog is sitting on the topmost step that is the first step.The frog jumps 3 step down and then jumps 2 step up . In how many jumps will it reach the water level ? after reaching the water level the frog jumps 4 steps up and then 2 steps down in every move.In how many jumps will it return to the topmost step ?
1) the frog reaches the water level, the 9th step after 40 jumps.
2) The frog returns to the top after 24 jumps
Step-by-step explanation:
In how many jumps will it reach the water level?
The frog jumps 3 step down and 2 steps up ⇒ These are five steps
The direction we are moving is downwards we can ascribe this as positive and upwards as negative:
Therefore 3 steps down = + 3
and 2 steps up = -2
If we add these five steps together the resultant vector is
+ 3 + -2 = 3 - 2= 1
Therefore in each of the set of five jumps ( 3 down and 2 up), the frog gains 1 step.
If The frog is in the first step, it needs to move 8 steps to get to the 9th step
Therefore:
To gain 1 step requires = 5 jumps
Then 8 steps requires = 5 jumps × 8 steps/ 1 step
= 40 jumps
Therefore the frog gets to the 9th step after 40 jumps
After how many jumps does the frog get back to the top?
The frogs makes 4 jumps up and 2 jumps down
Upwards is positive (+)
Downwards negative (-)
+4 + - 2 = 4 - 2 = 2
There in every 4 plus 2 jumps ( 6 jumps) the frog gains 2 steps
To get back to the top from the water level ( 9th step) to the top (1st step), the frog requires 9 -1 = 8 steps
If 2 steps requires 6 jumps
Then 8 steps will require = 6 jumps × 8 steps/2 steps
= 24 jumps
Therefore the frog requires 24 jumps to get back to the top