Final answer:
When a body is projected vertically upward, the height reached and the velocity of projection can be determined using the equations of motion. The height, h, can be found using the equation h = u * t₁ - 0.5 * g * t₁², where u is the initial velocity and t₁ is the time taken to reach the maximum height. The velocity of projection, u, can be found using the equation u = g * t₁.
Step-by-step explanation:
When a body is projected vertically upward, the height reached and the velocity of projection can be determined using the equations of motion. Let's assume that the initial velocity of the body is u and the height is h.
During the ascent, the velocity of the body decreases due to the acceleration due to gravity (g), until it reaches a maximum height. The time taken to reach this maximum height, t₁, can be found using the equation:
u - g * t₁ = 0
This equation implies that the velocity of the body becomes zero at the maximum height.
After reaching the maximum height, the body starts descending. The time taken to reach the same height h during the descent, t₂, can be calculated using the equation:
u + g * t₂ = 0
To find the height h, we can use the equation of motion:
h = u * t₁ - 0.5 * g * t₁²
The velocity of projection can be found using the equation:
u = g * t₁