At the end of the ride up a steep hill, ken was at an elevation of 1600 meters above where he started. he figured out that he and his bicycle had accomplished 1,000,000 joules of work. if ken has a mass of 52 kg, what is the mass of his bicycle?

Step-by-step explanation:

first place)

in first place you must Know by definition that a joule is defined as the amount of work done by a constant force in a meter of length

and it is 1 J = 1 N ×m = 1 kg ×m/s² ×m= 1 Kg×m²/s²

now you can calculate the time done by ken and his bicycle

1000000 = 52kg×(1600)²/s² = 1000000= 133120000/s²⇒1000000s² = 133120000⇒s²= 133120000/1000000⇒ s² =133,12⇒s =√133,12 = 11,5 ≅12

12 s is the time that ken with his bicycle ride up to the mountain

second )

having the time you can calculate the work done by ken individually

52kg×(1600)²/(12)² =133120000/ (12)² = 924444,4 and this is the  work done by  ken

Now you must substract  the work done by ken and his bicycle from  the work  done by ken individually in order to know  the work of the bicycle

1000000 joules -924444,4 joules  = 75555,6 joules

Having this amount, you can calculate the mass of the bicycle

and it is 1 J = 1 N ×m = 1 kg ×m/s² ×m= 1 Kg×m²/s²

75555,6 = kg *(1600) ²/(12)²⇒ 75555,6 =17777,7kg⇒ Kg = 75555,6/17777,7  = 4,25 kg

the mass of the  ken's bicycle is 4,25 kg

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."