^Projectile thrown straight up
Suppose a body is projected upwards from the ground and with the velocity u. The characteristics of motion of such a body are as follows.
- The maximum height attained
- Time taken to go up (ascent) = Time taken to come down (descent)
- Time of flight
- For an object thrown straight upwards with u = 50 m/s\
- The speed of the body on return to the ground = speed with which it was thrown upwards
- When the height attained is not large, that is u is not large, the mass, the weight as well as the acceleration remain constant with time its speed, velocity, momentum, potential energy and kinetic energy change with time.
- Let m be the mass of the body. Then in going from the ground to the highest point, following changes take place.
- Change in speed = u
- Change in velocity = u
- Change in momentum = m u
Change in KE = Change in PE =
- On return to the ground the changes in these quantities are as follows:
- Change in speed = 0
- Change in velocity = 2 u
- Change in momentum = 2 mu
Change in KE = Change in PE = 0
- If the friction of air be taken into account, then the motion of the object thrown upwards will have the following properties:
- Time taken to go up (ascent) < time
taken to come down (descent)
- The speed of the object on return to the
ground is less than the initial speed. Same is true for velocity (magnitude), momentum (magnitude) and KE.
- Maxi height attained is less than .
- A part of the KE is used up in overcoming