Answer:
The maximum height is reached after 3.75 seconds.
Step-by-step explanation:
Assuming the deceleration due to gravity is unaided by air resistance, gravity causes the ball to lose vertical speed at the rate of 32 ft/s every second. The initial vertical speed of 120 ft/s will decline to zero when t satisfies ...
... 120 ft/s - (32 ft/s²)t = 0
... (120 ft/s)/(32 ft/s²) = t = 3.75 s
The ball will not go any higher after its vertical speed is zero.
Answer:
a) The length of its edge is 8 units.
b) The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
Step-by-step explanation:
a) The volume of a cube (), measured in cubic units, is defined by the following expression:
(1)
Where is the side length of the cube, measured in units.
If we know that , then the length of its edge is:
The length of its edge is 8 units.
b) The volume of a sphere (), measured in cubic units, that fits snugly inside this cube is defined by:
(2)
If we know that , then the volume of the sphere is:
The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube taken by the sphere is the ratio of the volume of the sphere to the volume of the cube. That is to say:
If we know that and
, then the fraction of the cube that is taken up by the sphere is:
The result in percentage form is calculated by multiplying the result above by 100.
The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.