A monkey standing on the ground wants to climb to the top of a vertical pole 13m tall.he climbs 5m to 1seconds and slips downward 3m in the next 1seconds..he again climbs 5m in 1sec ANd slips by 3m in the next second and so on..draw the x-t graph of his motion and hence find the time he will take to reach the top of the pole
Not physics until he jumps
To draw the x-t graph of the monkey's motion, we need to understand the pattern of his movements and divide them into intervals of time. Let's break down his actions:
1. Climbs 5m in 1 second.
2. Slips downward 3m in the next 1 second.
3. Repeats the same pattern.
Since he climbs 5m and then slips downward 3m, the net displacement for each cycle is 5m - 3m = 2m.
Now, let's plot the x-t graph:
1. Start at the origin (x = 0, t = 0).
2. The monkey climbs 5m in the first second, so we go up 5m on the y-axis. The new position is (0, 5).
3. In the next second, the monkey slips downward 3m, so we move down 3m on the y-axis. The position becomes (0, 2).
4. The monkey repeats the pattern in the next second: climbing 5m, so we go up 5m on the y-axis. The position becomes (0, 7).
5. In the following second, the monkey slips downward 3m, so we move down 3m on the y-axis. The position becomes (0, 4).
6. The pattern repeats again and again, creating a sequence of points on the x-t graph.
Now, let's find the time it will take the monkey to reach the top of the pole. Since the monkey climbs 5m in 1 second and the pole is 13m tall, it will take the monkey a total of (13m / 5m) * 1 second for each complete cycle.
In other words, the time it takes for the monkey to reach the top of the pole is equal to the time for one complete cycle multiplied by the number of cycles required to reach the top. The total displacement for each cycle is 2m, so the number of cycles required is (13m / 2m).
Using this information, we can calculate the total time taken:
Total time = (13m / 5m) * 1 second * (13m / 2m) cycles
Simplifying this expression, we get:
Total time = (13 * 13) / (5 * 2) seconds
Thus, the time it will take for the monkey to reach the top of the pole is 16.9 seconds (approximately).