Answer:
v = 10 m/s
Explanation:
Let's assume the wheel does not slip as it accelerates.
Energy theory is more straightforward than kinematics in my opinion.
Work done on the wheel
W = Fd = 45(12) = 540 J
Some is converted to potential energy
PE = mgh = 4(9.8)12sin30 = 235.2 J
As there is no friction mentioned, the remainder is kinetic energy
KE = 540 - 235.2 = 304.8 J
KE = ½mv² + ½Iω²
ω = v/R
KE = ½mv² + ½I(v/R)² = ½(m + I/R²)v²
v = √(2KE / (m + I/R²))
v = √(2(304.8) / (4 + 0.5/0.5²)) = √101.6
v = 10.07968...
Now the vertical velocity of the ball thrown at an angle 10° is given as
Voy(initial vertical velocity)= 30m/s x sin 10
Voy(initial vertical velocity)= 5.2m/s
Now the ball is decelerating with an acceleration due to gravity equivalent to 9.8m/s^2.
Let Vy be the final velocity and that is equal to zero in this case.
Now
Vy= Voy- tx9.8
Where t is the time at which the vertical velocity becomes 0.
Substituting the values we get
0= 5.2-tx9.8
9.8t=5.2
t=0.53 secs
Frequency and wavelength are inversely proportional.
A shorter wavelength implies a higher frequency.
