In: Physics
The projectile is projected vertically upwards. The acceleration on the particle is the acceleration due to gravity, g which is acting in the opposite direction of the particle, so the particle's velocity will decrease with time and after a certain height it will stop and returns.
At maximum height the velocity of the particle will be 0m/s and after that the particle start moving in opposite direction.
Therefore from Newton's equation
V = V0 - gt, here acceleration is negative since it is acting downward while the particle is moving up, V is the velocity of the particle at maximum height and v=0, also V0 is the initial velocity of the particle when it was launched.
Therefore 0 = 18 - 9.8t
t = 18/9.8
t = 1.84 s . This is the time taken fir the particle to reach maximum height.
Now the maximum height can be found out using the equation
V2 - Vo2 = - 2gs
0 - 182 = -2*9.8*s
324 = 19.6*s
S = 324/19.6
S = 16.53 m is the maximum height attained by the particle.