Answer:
the time Joshua travels 1 mile is 12.5 min
Explanation:
Let's start by finding the distance traveled on each lap,
Let's reduce everything to the SI system
R = 400 m
d = 1 mile (1609 m / 1 mile) = 1609 m
L = 2 pi R
L = 2 pi 400
L = 2513 m
Let us form a rule of proportions if 2 turns of Julian is 3 turns Joshua, for 1 turn of Joshua how many turns Julian took
lap Julian = 2/3 turn Joshua
Let's calculate what distance is the same for both of them since they are on the same track
1 lap = 2513 m
d. Julian = 2/3 2513 m
d Julian = 1675 m distance Joshua
Let us form the last rule of three or proportions if 1609 m you travel in 12 min how long it takes to travel 1675 m
t Julian = 1675/1609 12
t = 12.5 s
Since this is the distance Joshua travels, this is the time Joshua travels 1 mile
Answer:
D.) 1m/s
Explanation:
Assume the initial angle of the swing is 12.8 degree with respect to the vertical. We can calculate the vertical distance from this initial point to the lowest point by first calculate the vertical distance from this point the the pivot point:
where L is the pendulum length
The vertical distance from the lowest point to the pivot point 
is the pendulum length 2m
this means the vertical distance from this initial point to the lowest point is simply:
As the pendulum travel (vertically) from the initial point to the bottom point, its potential energy is converted to kinetic energy:
where m is the mass of the pendulum, g = 10 m/s2 is the constant gravitational acceleration, h = 0.05 is the vertical it travels, v is the pendulum velocity at the bottom, which we are trying to solve for.
The m on both sides of the equation cancel out
so D is the correct answer
No. Mechanical energy is not conserved. There's quite a bit of friction on the slide. So some of the potential energy is lost to heat on the way down, and the child arrives at the bottom with hot pants and less kinetic energy than you might expect.
