Final answer:
The pebble will touch the ground approximately 346 times when the bicycle travels 1 km.
Step-by-step explanation:
To find out how many times the pebble will touch the ground when the bicycle travels 1 km, we need to calculate the circumference of the tire. The circumference of a circle can be calculated using the formula C = 2*pi*r, where C is the circumference, pi is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
So, for the given tire with a radius of 46 cm, the circumference would be C = 2*pi*46 cm = 2*3.14159*46 cm = 289.026 cm.
Since the pebble touches the ground with each turn of the wheel, the total number of times it will touch the ground can be calculated by dividing the distance traveled (1 km = 100,000 cm) by the circumference of the tire:
Number of times pebble touches the ground = 100,000 cm / 289.026 cm = 346.02
Therefore, the pebble will touch the ground approximately 346 times when the bicycle travels 1 km.