Question

Consider a falling mass(m) under gravity(9.8m/s). Initial velocity of the mass is 5 m/s upwards. Derive expressions for the velocity and the position of the mass(m) in terms of time and initial velocity/position of the mass. a) -How long will the mass take to reach the maximum height position? b)- What would be the maximum height the mass reach relative to its initial position?

Answer 1

a) 0.51 s

b) 1.275m

Step-by-step explanation:

using equation of linear motion

v=u+gt...........................(1)

`v^(2) -u^(2)=2gh`...........(2)

`s=ut+(1)/(2) gt^2`.......(3)

a) as the ball is thrown upward -ve 'g' will be acting on the body

as the body reaches to the maximum height the final velocity(v) becomes

zero so from equation (1)

0=5-9.8t

`t=(5)/(9.8)`

t=0.51s

b) Now for maximum height calculation using equation (2)

`v^(2) -u^(2)=2gh`

v=0

`h=(-u^2)/(2g)`

`h=(-5^2)/(2*-9.8)`

h=1.275m