A projectile is shot straight up leaving the ground at 30 m/s. If air...

Question

A projectile is shot straight up leaving the ground at 30 m/s. If air resistance is ignored:
a. What will be the speed of the object when it reaches a height of 15 m? Solve using energy.

b. Same question as a), but this time solve using kinematics equations.

c. If the projectile in the previous examples has a mass of 2.0 kg and reached the height of 15 m, but only had velocity of 22.2 m/s, how much energy was dissipated as heat due to air resistance?

 

Answers: 25m/s, 113J

Answer 1

a) Ki+Ui=Kf+Uf

initial potential Ui=0

0.5*m*vi^2=0.5*m*vf^2+m*g*h

 

The masses cancel.

 

0.5*vf^2+g*h=0.5*vi^2

 

solve for vf.

 

 

b) if you multiply both sides by 2 and bring the g*h term on the other side you get the standand kinematic equation.

vf^2=vi^2-2*g*h

vf=24.6m/s.

 

c) Total Energy is Ki=0.5*2*vi^2=900Joules

at 15m is the speed is 22.2m/s the energy is Kf+Uf=0.5*m*vf^2+m*g*h=786.8

 

The difference is energy lost due to dissipation.   900-787=113Joules