Answer:
Time = t = 6.62 s
Explanation:
Given data:
Height = h = 215 m
Initial velocity = 
= 0 m/s
gravitational acceleration = g = 9.8 m/s²
Time = t = ?
According to second equation of motion
As initial velocity is zero, So the first term of right hand side of above equation equal to zero.
t² = 
t =
t = 
t = 6.62 s
Answer:
The mass of the cargo is 
Explanation:
From the question we are told that
The radius of the spherical balloon is 
The mass of the balloon is 
The volume of the spherical balloon is mathematically represented as
substituting values
The total mass the balloon can lift is mathematically represented as
where 
is the density of helium with a value of
and 
is the density of air with a value of
substituting values
Now the mass of the cargo is mathematically evaluated as
Explanation:
For each object, the initial potential energy is converted to rotational energy and translational energy:
PE = RE + KE
mgh = ½ Iω² + ½ mv²
For the marble (a solid sphere), I = ⅖ mr².
For the basketball (a hollow sphere), I = ⅔ mr².
For the manhole cover (a solid cylinder), I = ½ mr².
For the wedding ring (a hollow cylinder), I = mr².
If we say k is the coefficient in each case:
mgh = ½ (kmr²) ω² + ½ mv²
For rolling without slipping, ωr = v:
mgh = ½ kmv² + ½ mv²
gh = ½ kv² + ½ v²
2gh = (k + 1) v²
v² = 2gh / (k + 1)
The smaller the value of k, the higher the velocity. Therefore:
marble > manhole cover > basketball > wedding ring
Answer:
Total momentum = 50kgm/s
Explanation:
<u>Given the following data;</u>
Mass, M1 = 5kg
Mass, M2 = 7kg
Velocity, V1 = 10m/s
Velocity, V2 = 0m/s (since it's at rest).
To find the total momentum;
Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
The law of conservation of momentum states that the total linear momentum of any closed system would always remain constant with respect to time.
Total momentum = M1V1 + M2V2
Substituting into the equation, we have;
Total momentum = 5*10 + 7*0
Total momentum = 50 + 0
<em>Total momentum = 50 kgm/s</em>
<em>Therefore, the total momentum of the bowling ball and the putty after they collide is 50 kgm/s. </em>
