Find the time th it takes the projectile to reach its maximum height h. express th in terms of v0, θ, and g (the magnitude of the acceleration d

An object thrown in air moving under the influence of gravitational force is known as projectile.

The projectile is thrown with an initial velocity at an angle with the horizontal. The initial velocity can be resolved in to horizontal and vertical components.

Here, is the horizontal component of initial velocity, is the initial velocity of the projectile, and is the angle by which the projectile is thrown with respect to the ground.

The vertical component of initial velocity of the projectile is,

Here, is the vertical component of initial velocity.

At maximum height the vertical velocity of the projectile momentarily goes to zero.

To calculate the time for maximum height is,

Here, is the velocity of the projectile at maximum height, g is the acceleration due to gravity, and is the time for maximum height reached by the projectile.

Substitute

The vertical velocity at an instant at the maximum height,

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