# The energy of a ball shot upwards

Homework Statement:
The ball with a mass of 200g is shot up with the instantaneous velocity of 14 m/s.
a) Determine the mechanical energy at the point of release
b) Find the speed of the ball after it has travelled for 0.2s
c) What is the kinetic energy of the ball after 0.2s
d) Use the conservation of energy principle to determine the max height the ball reaches
Relevant Equations:
E(gravity)=mgh
E(kinetic)=1/2mv^2
E(mech1)=E(g)+E(k)
E(mech1)=E(mech2)
a) E(mech)=E(k)+E(g)
E(mech)=1/2mv^2+(0.2)(9.8)(0)
E(mech)=19.6 J

b) E(mech1)=E(mech2)
E(k)+E(g)=E(k)+E(g)
E(g)=E(k)+E(g)
0=1/2mv^2+(mgh)
*No height is given so I can't solve using this method. It says instantaneous velocity meaning the velocity at 0.2s is different.

c) E(k)=1/2mv^2
E(k)=1/2(0.2)(i would use the velocity from q.b)^2

d) E(mech1)=E(mech2)
E(k)+E(g)=E(k)+E(g)
E(g)=E(k)
mgh=1/2mv^2
h=v^2/2g
h=(how would i calculate v?)^2/2(9.8)

So, I am stuck on how to calculate a few values. I can't use kinematics as this is the energy unit.

Mentor
So, I am stuck on how to calculate a few values. I can't use kinematics as this is the energy unit.
I'm pretty sure that you are allowed to use kinematics to find the velocity a given time. Conservation of energy method does not consider time in its application, so clearly you need another method for that (hence: kinematics).

I'm pretty sure that you are allowed to use kinematics to find the velocity a given time. Conservation of energy method does not consider time in its application, so clearly you need another method for that (hence: kinematics).

I still wouldn't be able to calculate velocity for part b by using kinematics as I have 3 missing values (no acceleration, no final velocity, and no displacement). Would I have to assume that the velocity is constant?

Mentor
I still wouldn't be able to calculate velocity for part b by using kinematics as I have 3 missing values (no acceleration, no final velocity, and no displacement). Would I have to assume that the velocity is constant?
Presumably the ball is assumed to be moving close to the Earth's surface. So what forces are acting on the ball?