Question

A man is climbing a pole 100 feet high. Each minute he climbs up 15 feet but slips down 10 feet in the next minute. How many minutes will he take to reach the top of the pole?

Answer 1

Hint- Speed of an object is the magnitude of the change of its position.
The average speed of a body in a certain time interval is the distance covered by the body in that time interval divided by time. So if a particle covers a certain distance s in a time \[{t_1}\] to \[{t_2}\], then the average speed of the body is:\[v = \dfrac{s}{{{t_2} - {t_1}}}\]
Average speed =Total distance/Total time. \[\]

Complete step-by-step answer:
It is given that the man is climbing a pole 100 feet high, each minute he climbs up 15 feet but slips down 10 feet in the next minute.
Therefore, the man climbs 15 feet in the 1st minute and slips down 10 feet in the next minute.
That is, in the first 2 minutes the man actually climbs (15-10) = 5 feet.
Then the average speed of the man is \[\dfrac{5}{2}{\text{feet / min}}\]
So he climbs in one minute is \[\dfrac{5}{2}{\text{feet}}\].
But in the last minute he climbs 15 feet as he goes on the top of the pole so there is no slip.
The time required to reach the top of the pole is,
\[ = \dfrac{{100 - 15}}{{\dfrac{5}{2}}} + 1\]
\[ = \dfrac{2}{5} \times 85 + 1\]
\[ = 2 \times 17 + 1\]
\[ = 35\min \]
Hence, he will take 35 minutes to reach the top of the pole.

Note: Speed is a scalar quantity which means it has no direction. It denotes how fast an object is moving. If the speed of the particle is high it means the particle is moving fast and if it is low, it means the particle is moving slow.