Apply this kinematics equation for the particle's vertical motion:
D = Vt + 0.5At²
D = vertical distance traveled, t = time, V = initial vertical velocity, A = vertical acceleration
Given values:
D = 49m
V = 34.3m/s
A = -9.81m/s²
Plug in and solve for t:
49 = 34.3t - 4.905t²
4.905t² - 34.3t + 49 = 0
Use the quadratic roots formula to find the values of t:
t ≈ 2, 5
The particle reaches a height of 49m at t = 2s & t = 5s
