Question

A ball is projected upward at time t = 0.0 s, from a point on a roof 90 m above the ground. The ball

rises, then falls and strikes the ground. The initial velocity of the ball is 29.7 m/s. Consider all
quantities as positive in the upward direction. The velocity of the ball when it is 34 m above the
ground is closest to:

Answer 1

Velocity 44.5 m/s

Step-by-step explanation:

Given:

t₀ = 0.0 s

H₀ = 90 m

V₀ = 29.7 m/s

h = 34 m

g = 9.8 m/s²

___________

V- ?

Ball motion equation:

h = H₀ + V₀·t - g·t² / 2

34 = 90 + 29.7·t - 9.8·t² /2

4.9·t² - 29.7·t - 56 = 0

Time:

t ≈ 7.57 s

Velocity:

V = V₀ - g·t

V = 29.7 - 9.8·7.57 ≈ - 44.5 m/s

The "-" sign indicates that the ball is moving down with a speed whose modulus is equal to 44.5 m/s