a cannonball is fired with a speed of 76 m/s from the top of a cliff. It strikes the plane below with a speed of 89 m/s. if we neglect air friction, how high is the cliff

Assuming the cannonball is fired horizontally, its horizontal velocity stays at a constant 76 m/s. At the point it hits the ground, it has a speed of 89 m/s, so if its vertical velocity at that moment is , we have

(taking the negative square root because we take the downward direction to be negative)

Recall that

where and are the initial and final velocities, respectively; is the acceleration; and is the change in position of a body. In the cannonball's case, it starts with 0 vertical velocity and is subject to a downward acceleration with magnitude . So we have

(which is negative because we take the cannonball's starting position at the top of the cliff to be the origin) so the cliff is about 109 m high.

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there are no components of a physical goal mentioned on the list of choices that you've provided.