Answer: 150.427 K
Explanation:
The complete question is as follows:
The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of
. HooRU's surface area is
and the emissivity of its surface is
. Ignore the radiation HooRU absorbs from the cold universe. What is HooRU's temperature?
This problem can be solved by the Stefan-Boltzmann law for real radiator bodies:
(1)
Where:
is the energy radiated by HooRU
is the Stefan-Boltzmann's constant.
is the Surface of the robot
is the robot's emissivity
is the effective temperature of the robot (its surface absolute temperature) in Kelvin
So, we have to find
from (1):
(2)
Finally:
Arrhenius' equation relates the dependence of rate constant of a chemical reaction to the temperature. The equation below is the Arrhenius equation

where k is the rate constant, T is the absolute temperature. As the temperature of the system increases, the rate constant also increases and vice versa.
<u>Answer:</u> The ball is travelling with a speed of 5.5 m/s after hitting the <u>bottle.</u>
<u>Explanation:</u>
To calculate the speed of ball after the collision, we use the equation of law of conservation of momentum, which is given by:

where,
are the mass, initial velocity and final velocity of ball.
are the mass, initial velocity and final velocity of bottle.
We are given:

Putting values in above equation, we get:

Hence, the ball is travelling with a speed of 5.5 m/s after hitting the bottle.
Answer:
d.
Explanation:
Since the dart's initial speed v at angle has both vertical and horizontal components v₀sinθ and v₀cosθ respectively, the vertical component of the speed continues to decrease until it hits the target. It's displacement ,s is gotten from
s = y - y₀ = (v₀sinθ)t - 1/2gt² where y₀ = 0 m
y - 0 = (v₀sinθ)t - 1/2gt²
y = (v₀sinθ)t - 1/2gt²
which is the parabolic equation for the displacement of the dart.
Note that the horizontal component of the dart's velocity does not change during its motion.
Since the target falls vertically, with initial velocity u = 0 (since it was stationary before the string cut), it's displacement ,s' is gotten from
s' = y - y₀' = ut - 1/2gt² where y₀' = initial height of target above the ground
= (0 m/s)t - 1/2gt²
= 0 - 1/2gt²
y - y₀' = - 1/2gt²
y = y₀' - 1/2gt²
which is the parabolic equation for the displacement of the target.
The equation for both the displacement of the dart and the target can only be gotten if we considered vertical motion. So, the displacement component of both the dart and target are both vertical.
So, the answer is d.