Question

A physics student standing on the edge of a cliff throws a stone vertically downward with an initial speed of 10 m/s. The instant before the stone hits the ground below, it is traveling at a speed of 30.0 m/s. If the physics student were to throw the rock horizontally outward from the cliff instead, with the same initial speed, what is the magnitude of the velocity of the stone just before it hits the ground?

A) 10 m/s
B) 20 m/s
C) 30 m/s
D) 40 m/s
E) the height of the cliff is needed to answer the question

Answer 1

When the stone is thrown horizontally outward from the cliff, the magnitude of the velocity of the stone just before it hits the ground can be calculated using the Pythagorean theorem. In this case, it will be 30 m/s.

Step-by-step explanation:

When the stone is thrown vertically downward, the only force acting on it is gravity. It accelerates due to gravity and increases its speed as it falls. When the stone hits the ground, it has a speed of 30.0 m/s.

If the stone is thrown horizontally outward from the cliff, it will have the same initial speed of 10 m/s. However, in this case, the stone will have both a horizontal and a vertical velocity component. The vertical velocity will be due to gravity, while the horizontal velocity will remain constant. The magnitude of the velocity of the stone just before it hits the ground can be calculated using the Pythagorean theorem:

Velocity total = √(Velocity horizontal)2 + (Velocity vertical)2

Since the stone is thrown horizontally, the vertical velocity will be equal to the final vertical velocity of the stone thrown vertically downward. Therefore, the magnitude of the velocity of the stone just before it hits the ground will be 30 m/s, which is option C.