Answer to Question #105239 in Classical Mechanics for Anika Roejkjaer

Question

A ball of mass 100g is thrown vertically upwards from a point 2m above ground level with a speed of 14m/s.
a. With an origin at ground level, find the total mechanical energy of the ball when it is travelling at speed v m/s at a heigh h m.
b. Assuming that mechanical energy is conserved show that v^2+20h=236
c. Calculate the greatest height reached by the ball
d. Calculate the speed with which the ball hits the ground

Answer 1

a)

$$E=0.5mv^2+mgh$$

b)

$$0.5mv^2+m(10)h=0.5m(14)^2+m(10)(2)$$

$$v^2+20h=(14)^2+2(10)(2)=236$$

c) It will be when speed is zero:

$$20H=236$$

$$H=11.8\ m$$

d)It will be when height is zero:

$$v^2=236$$

$$v=15.4\frac{m}{s}$$