The football team is selling mulch as a fundraiser. Which two options are
2 answers:
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(a) 296.6 m
The motion of the stone is the motion of a projectile, thrown with a horizontal speed of
and with an initial vertical velocity of
where we have put a negative sign to indicate that the direction is downward.
The vertical position of the stone at time t is given by
(1)
where
h is the initial height
g = -9.81 m/s^2 is the acceleration due to gravity
The stone hits the ground after a time t = 6.00 s, so at this time the vertical position is zero:
y(6.00 s) = 0
Substituting into eq.(1), we can solve to find the initial height of the stone, h:
(b) 176.6 m
The balloon is moving downward with a constant vertical speed of
So the vertical position of the balloon after a time t is
and substituting t = 6.0 s and h = 296.6 m, we find the height of the balloon when the rock hits the ground:
(c) 198.2 m
In order to find how far is the rock from the balloon when it hits the ground, we need to find the horizontal distance covered by the rock during the time of the fall.
The horizontal speed of the rock is
So the horizontal distance travelled in t = 6.00 s is
Considering also that the vertical height of the balloon after t=6.00 s is
The distance between the balloon and the rock can be found by using Pythagorean theorem:
(di) 15.0 m/s, -58.8 m/s
For an observer at rest in the basket, the rock is moving horizontally with a velocity of
Instead, the vertical velocity of the rock for an observer at rest in the basket is
Substituting time t=6.00 s, we find
(dii) 15.0 m/s, -78.8 m/s
For an observer at rest on the ground, the rock is still moving horizontally with a velocity of
Instead, the vertical velocity of the rock for an observer on the ground is now given by
Substituting time t=6.00 s, we find
Before answering this question, first we have to understand the effect of ratio of surface area to volume on the rate of diffusion.
The rate of diffusion for a body having larger surface area as compared to the ratio of surface area to volume will be more than a body having less surface area. Mathematically it can written as-
V∝ R [ where v is the rate of diffusion and r is the ratio of surface area to volume]
As per the question,the ratio of surface area to volume for a sphere is given
The surface area to volume ratio for right circular cylinder is given
Hence, it is obvious that the ratio is more for right circular cylinder.As the rate diffusion is directly proportional to the surface area to volume ratio,hence rate of diffusion will be more for right circular cylinder.
Hence the correct option is B. The rate of diffusion would be faster for the right cylinder.