The equation is derived from the conservation of energy, specifically from potential energy stored at a given height in a gravitational field.
When potential energy is completely converted to kinetic energy you have:
(mv^2)/2=mgh divide both sides by the mass m
v^2/2=gh multiply both sides by 2
v^2=2gh take the square root of both sides
v=√(2gh) and working with imperial units for acceleration due to gravity, g=-32ft/s^2
v=√(-64h) but the change of h as it falls is negative h so
v=-√(64h) so if an object falls from a height of 88ft we have:
v=-√(64*84)
v=-√5376
v≈-73.32 ft/sec (to the nearest hundredth of a foot per second)
Note that this is the velocity, it is negative 73.32 ft/sec.
The question inadvertently asked for velocity and provided answers for SPEED. Velocity is a vector and has both magnitude and direction, whereas speed just has magnitude.
So its final speed is 73.32 ft/sec
So if they actually wanted velocity none of their answers is correct :P
Answer: b
Step-by-step explanation:
Since the problem is given all the total walking distance, the first thing we are going to do is find the total distance in the map:
Now that we have the distance in the map, we can establish a ratio between the walking distance and the distance in the map:
We can conclude that each inch the map represents 0.5 miles of walking distance.
I:a*b=48
II:a/b=3
II': a=3b
insert into I:
3b*b=48
b*b=16
b=4
insert b=4 into I:
a*4=48
a=12
solution: a=12, b=4
12*4=48
12/4=3