Respuesta :
Explanation:
The given data is as follows.
mass (m) = 5 kg
Height of tower = 15 m
u = 7 m/s
air resistance = 610 v
(a) Now, differential equation for the given mass which is thrown vertically upwards is as follows.
[tex]m \frac{d^{2}x}{dt^{2}}[/tex] = F
-bv = Fr
Here, mg is downwards due to the force of gravity.
[tex]\frac{md^{2}x}{dt^{2}} = bv - mg[/tex]
[tex]\frac{md^{2}x}{dt^{2}} + b \frac{dx}{dt} + mg[/tex] = 0
Hence, the differential equation required to solve the problem is as follows.
[tex]\frac{md^{2}x}{dt^{2}} + b \frac{dx}{dt} + mg[/tex] = 0
(b) When final velocity of the object is equal to zero then the object will reach towards its maximum height and it will start to fall downwards.
F = [tex]\frac{md^{2}x}{dt^{2}}[/tex]
= 0
Therefore, the object reach its maximum height at v = 0.
