Projectile motion

Question

At t=0 a hot ballon moving upwards at 10 m/s drops a sandbag as the ballon is 10 meter above ground a) what is the maximum height reached by the sandbag ? B) how long does it take the sandbag to reach the ground

Answer 1

h₀ = 10 m

v₀ = 10 m/s

g = 9.8 m/s²

h(t) = -gt²/2 + v₀t + h₀

h(t) = -4.9t² + 10t + 10

(a)

Maximum height is at the vertex of the h-vs.-t parabola, which is at

t = -10 / [2(-4.9)] s = ? s

Evaluate h(t) at this value of t to get h_max.

(b)

Set h(t)=0 and find t using the quadratic formula. You will get two values for t, one positive and one negative. The positive value is the correct solution, since t starts at t=0.