Answer to Question #1239 in Mechanics | Relativity for danica

Question

A juggler throws a ball from height of 0.950 m with a vertical velocity of +4.25 m/s and misses it on the way down. What is its velocity when it hits the ground?

Answer 1

We use the equations of the motion:
h = h₀ +v₀t - gt²/2;
v = v₀ - gt.


h₀ = 0.95
v₀ = 4.25 m/s
h = 0

0 = 0.95 +4.25t - 10t²/2
5t² - 4.25t - 0.95 = 0
D = 4.25² + 5*0.95*4 = 37
t₁ = (4.25+6.08) / 10 = 1.03
t₂ = -0.18 - out of sense.

v = 4.25 - 1.03*10 = -6.05
Answer:
The velocity would be equal to 6.05 m/s and its vector is directed downward.