Maximum Height Formula

A projectile is an object that is given an initial velocity, and is acted on by gravity. The maximum height of the object is the highest vertical position along its trajectory. The maximum height of the projectile depends on the initial velocity v0, the launch angle θ, and the acceleration due to gravity. The unit of maximum height is meters (m).

H = maximum height (m)

v0 = initial velocity (m/s)

g = acceleration due to gravity (9.80 m/s2)

θ = angle of the initial velocity from the horizontal plane (radians or degrees)

Maximum Height Formula Questions:

1) A fire fighter aims a fire hose upward, toward a fire in a skyscraper. The water leaving the hose has a velocity of 32.0 m/s. If the fire fighter holds the hose at an angle of 78.5°, what is the maximum height of the water stream?

Answer: The water droplets leaving the hose can be treated as projectiles, and so the maximum height can be found using the formula:

Question:   H = ??.? m

.2) An athlete in a high jump competition leaves the ground at a velocity of 5.80 m/s, and an angle of 87.4°. What is the maximum height of the athlete’s center of mass?

Question:  H = ?.??m 