To solve this problem, we must determine how many jumps the frog needs to make to get out of the 30-meter deep well.
- The frog jumps up \(70 \text{ cm}\) on each jump and then slides back down \(30 \text{ cm}\).
- The effective height gained after each jump is: \(70 \text{ cm} - 30 \text{ cm} = 40 \text{ cm}\)
- First, convert the depth of the well to centimeters: \(30 \text{ m} = 3000 \text{ cm}\)
- Determine how many effective jumps of \(40 \text{ cm}\) each are needed to reach just below the rim of the well: \(\frac{3000 \text{ cm}}{40 \text{ cm per jump}} = 75 \text{ jumps}\)However, with 75 full jumps, let's consider the scenario:
- After 74 jumps, the frog would have climbed: \(74 \times 40 \text{ cm} = 2960 \text{ cm}\)
- This means at the start of the 75th jump, the frog is 2960 cm up, requiring one more \(70 \text{ cm}\) jump to finish the climb without slipping back again.
Therefore, the minimum number of jumps required for the frog to completely get out of the well is 75.
Summary: The frog effectively gains \(40 \text{ cm}\) per jump, and after 74 jumps, it is at 2960 cm. The 75th jump allows it to reach the top.
Important Questions from Quick Math
If the numerical data is represented by pictures in which 1 bucket represents 1000 quintle milk then how many buckets are needed to represent 6500 quintle milk ?
The scale of the map is 20 km for 1 cm. What area of the country will be represented on the map whose area is 60,000 km 2 ?
A biology class at Central High School predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2021 was estimated to be 50 animals. If P represents the population n years after 2021, then which of the following equations represents the class model of the population over time?
In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English, The number of Indians who can speak English is
A boy plays with a ball and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5 th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing ?
