Derive the equation of time taken by projectile partical to reach at maximum height. (class 11)
Answers
Answer:
The expressions for the maximum height, time of ascent, time of descent, time of flight in the case of vertical projection can be easily determined by using a diagram of the projectile. In this case, we will make use of the vertical component of the velocity, as we will be deriving the expressions for the above-mentioned parameters belonging to a vertical projection.
Complete step by step answer:
Let a projectile be projected at an angle θ
with the initial velocity u.
From the diagram, we get,
ux=xt⇒x=ux×t
Substitute the values in the above equation.
x=ucosθ×t⇒t=xucosθ
Maximum height
The height reached by the body when projected vertically upwards where the vertical velocity is zero.
Using the law of motion equation we will further continue to find the expression of maximum height.
H=uyt+12gt2⇒H=usinθ(usinθg)−12g(usinθg