Answer:
10s
Explanation:
If it took Beatrice 25 seconds to complete the race
Distance = 100 meter
Beatrice speed = 100/25
= 4m/s
If Alice runs at a constant speed and crosses the finish line $5$ seconds, she must have completed the race in 20s (25 -5).
Her speed where constant
= 100/20
= 5 m/s
It would take Alice
= 50/5
= 10s
It would take Alice 10s to run $50$ meters.
Answer:
T = 188.5 s, correct is C
Explanation:
This problem must be worked on using conservation of angular momentum. We define the system as formed by the fan and the paper, as the system is isolated, the moment is conserved
initial instant. Before the crash
L₀ = r m v₀ + I₀ w₀
the angular speed of the fan is zero w₀ = 0
final instant. After the crash
L_f = I₀ w + m r v
L₀ = L_f
m r v₀ = I₀ w + m r v
angular and linear velocity are related
v = r w
w = v / r
m r v₀ = I₀ v / r + m r v
m r v₀ = (I₀ / r + mr) v
v = 
let's calculate
v = 
v = 
v = 0.02 m / s
To calculate the time of a complete revolution we can use the kinematics relations of uniform motion
v = x / T
T = x / v
the distance of a circle with radius r = 0.6 m
x = 2π r
we substitute
T = 2π r / v
let's calculate
T = 2π 0.6/0.02
T = 188.5 s
reduce
t = 188.5 s ( 1 min/60 s) = 3.13 min
correct is C
Answer:
The temperature of the metal is 
Explanation:
From the question we are told that
The mass of the metal is 
The specific heat of the metal is 
The mass of the oil is 
The temperature of the oil is 
The specific heat of oil is 
The equilibrium temperature is 
According to the law of energy conservation
Heat lost by metal = heat gained by the oil
So
The quantity of heat lost by the metal is mathematically represented as

=> 
Where
the temperature of metal before immersion
The negative sign show heat lost
The quantity of gained t by the metal is mathematically represented as

=> 
So

substituting values

=> 
Answer: Speed = 4 m/s
Explanation:
The parameters given are
Mass M = 60 kg
Height h = 0.8 m
Acceleration due to gravity g= 10 m/s2
Before the man jumps, he will be experiencing potential energy at the top of the table.
P.E = mgh
Substitute all the parameters into the formula
P.E = 60 × 9.8 × 0.8
P.E = 470.4 J
As he jumped from the table and hit the ground, the whole P.E will be converted to kinetic energy according to conservative of energy.
When hitting the ground,
K.E = P.E
Where K.E = 1/2mv^2
Substitute m and 470.4 into the formula
470.4 = 1/2 × 60 × V^2
V^2 = 470.4/30
V^2 = 15.68
V = square root (15.68)
V = 3.959 m/s
Therefore, the speed of the man when hitting the ground is approximately 4 m/s
In order to find the force (F), you would have to use the formula for it:
F=ma
where m is mass and a is acceleration.
In the problem, the mass is 2.85kg and the acceleration is 4.9m/s^2.
Therefore,
F=2.85kg(4.9m/s^2)
F=13.965kg(m/s^2)
Since N=kg(m/s^2)
F=13.965N
And because the problem requires that we use only 2 significant figures,
F=13N
Therefore, the student must exert 13N of force.