Velocity physics help

Question

A boy throws a ball up in the air with a velocity of 7 m/s when they are standing at the edge of a cliff 20 m high. If the ball falls and lands at the base of the cliff, what is the velocity of the ball when it lands? How long was the ball in the air?

Answer 1

Up is positive y. v₀ = 7 m/s, y-y₀ = -20 m (note the sign), a = -9.8 m/s² Know 3/5 variables with 2 independent equations.

We can solve for v(landing) using the autonomous (no t equation)

2ad = v² - v₀² solving for v = sqrt(2ad + v₀²) (Note that the negative square root is correct!)

You can then find time in the air from the definition of constant a: a = (v-v₀)/t or t = (v-v₀)/a

Good luck.