Projectile Motion

See attached file.

A spear is thrown upward from a cliff 48 m above the ground. Given an initial speed of 24 m/s at an angle of 30º to the horizontal,
a. how long is the spear in flight?

Solution: The Initial vertical velocity of the spear is:

The time the spear will rise at the peak of the projectile is:

The peak height of the spear with reference from the cliff is:

The time of the fall of the spear to the ground below the cliff is:

The total time of flight of the spear is:

b. what is the magnitude and direction of the spear's velocity just before it hits the ground?

Solution: The final vertical velocity is:

The horizontal velocity is constant all throughout. So we have:

The final velocity is:

The direction from the horizontal is:

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