Question

A rock climber climbs a hill of height 200m at the rate of 3 m/s. If he starts climbing from 20m above the ground, then find the following :
(i) What is the total distance he needs to trek to climb to the top of the hill?
(ii) What is the time taken by him to reach the hilltop?
(iii) If he covered half of the distance at 3 m/s and remaining distance at 2 m/s, find the total time taken by him to climb the hill. [3 MARKS]

Answer 1

Each question: 1 Mark

Rate at which climber climbs the hill = 3 m/s

Total distance to be climbed by the climber = 200m - 20m = 180m

The time required by the climber to reach the top of the hill is

$=\frac{180}{3}$

= 60 seconds

Hence, the climber will climb the hill in 60 seconds.

It is given that he covered half of the distance at 3 m/s and the remaining half at 2 m/s.

Total distance to be covered = 180m

Distance covered with speed 3 m/s = $\frac{180}{2}$
= 90m

Distance covered with speed 2 m/s
= 180-90 = 90m

Time taken to cover the first 90m = $\frac{90}{3}$
= 30 seconds

Time taken to cover the last 90m = $\frac{90}{2}$
= 45 seconds

The total time taken to climb to the top of the hill = 30 + 45 = 75 seconds