A bicyclist wants to make it from one building to the next. The first building he is standing on is 20 m tall. The building he wants to reach is 12 m tall. He is moving at 4 m/s and the gap between both buildings is 5 m. Will he make it?
Please just show me how to break down this 2D problem. I have been struggling with understanding it.
d = 0.5g*t^2 = 20-12 = 8 m.
4.9t^2 = 8
t^2 = 1.63
t = 1.28 s. = Fall time.
Range = V*t = 4m/s * 1.28s = 5.12 m.
5.12m > 5 m. Therefore, he will make it.
To break down this 2D problem, we need to consider the motion of the bicyclist in the vertical direction (up and down) and the horizontal direction (left and right). Let's analyze both separately.
Vertical motion:
1. Calculate the height difference between the two buildings: 20 m - 12 m = 8 m.
2. We know that the bicyclist's maximum jump height is 5 m, which means he cannot jump over a gap higher than 5 m.
3. Since the height difference is 8 m, the bicyclist will not be able to jump directly from one building to the other.
Horizontal motion:
1. Calculate the horizontal distance between the two buildings, which is given as 5 m.
2. The bicyclist is moving at a speed of 4 m/s.
3. To determine if the bicyclist will make it, we need to calculate the time it will take for him to traverse the horizontal distance between the buildings.
Time = Distance / Speed
Time = 5 m / 4 m/s = 1.25 seconds.
Combining both motions:
Based on the analysis above, we can conclude that although the bicyclist can cover the horizontal distance in 1.25 seconds, he cannot clear the vertical height difference of 8 m. Therefore, he will not be able to make it to the other building.