A hiker throws a stone from the upper edge of a vertical cliff. The stone's initial velocity is 25.0 m/s directed at 40.0° with the face of the cliff, as shown in the figure.The stone hits the ground 3.75 s after being thrown.How fast is the stone moving just before it hits the ground?Ignore air friction and express your answer in m/s.

To solve this problem, we need to break it down into two parts: the horizontal and vertical components of the stone's velocity.

Step 1: Determine the initial horizontal and vertical velocities. The initial velocity of the stone is given as 25.0 m/s at an angle of 40.0°. We can use trigonometry to find the horizontal and vertical components of this velocity.

Vx (horizontal velocity) = V * cos(θ) = 25.0 m/s * cos(40.0°) = 19.15 m/s Vy (initial vertical velocity) = V * sin(θ) = 25.0 m/s * sin(40.0°) = 16.07 m/s

Step 2: Determine the final vertical velocity. The stone is under the influence of gravity, which will accelerate it downwards at a rate of 9.8 m/s². We can use the equation of motion to find the final vertical velocity:

Vf = Vi + a*t where Vf is the final vertical velocity, Vi is the initial vertical velocity, a is the acceleration due to gravity, and t is the time.

Vf = 16.07 m/s - (9.8 m/s² * 3.75 s) = -20.25 m/s

Note: The velocity is negative because the stone is moving downwards.

Step 3: Determine the total final velocity. The stone's total final velocity is the vector sum of its horizontal and vertical velocities. We can use the Pythagorean theorem to find this:

Vtotal = sqrt((Vx)² + (Vf)²) = sqrt((19.15 m/s)² + (-20.25 m/s)²) = 27.8 m/s

So, the stone is moving at 27.8 m/s just before it hits the ground.

To solve this problem, we need to break it down into two parts: the horizontal and vertical components of the stone's velocity.

Step 1: Determine the initial horizontal and vertical velocities. The initial velocity of the stone is given as 25.0 m/s at an angle of 40.0°. We can use trigonometry to find the horizontal and vertical components of this velocity.

Vx (horizontal velocity) = V * cos(θ) = 25.0 m/s * cos(40.0°) = 19.15 m/s Vy (initial vertical velocity) = V * sin(θ) = 25.0 m/s * sin(40.0°) = 16.07 m/s

Step 2: Determine the final vertical velocity. The stone is under the influence of gravity, which will accelerate it downwards. We can use the equation of motion to find the final vertical velocity:

Vf = Vi + at where Vf is the final velocity, Vi is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and t is the time (3.75 s).

Vf = 16.07 m/s - (9.8 m/s² * 3.75 s) = -20.28 m/s

The negative sign indicates that the velocity is directed downwards.

Step 3: Determine the total final velocity. The total final velocity is the vector sum of the horizontal and vertical velocities. We can use the Pythagorean theorem to find this:

V_total = sqrt((Vx)² + (Vf)²) = sqrt((19.15 m/s)² + (-20.28 m/s)²) = 27.9 m/s

So, the stone is moving at 27.9 m/s just before it hits the ground.

To solve this problem, we need to break it down into two parts: the horizontal and vertical components of the stone's motion.

Step 1: Determine the initial velocities in the horizontal and vertical directions.

The initial velocity (v0) is given as 25.0 m/s at an angle of 40.0° from the horizontal. We can use trigonometry to find the horizontal (v0x) and vertical (v0y) components of this velocity:

v0x = v0 * cos(40.0°) = 25.0 m/s * cos(40.0°) = 19.15 m/s v0y = v0 * sin(40.0°) = 25.0 m/s * sin(40.0°) = 16.07 m/s

Step 2: Determine the final velocity in the vertical direction.

We know that the stone hits the ground 3.75 s after being thrown. We can use the equation of motion to find the final vertical velocity (vfy):

vfy = v0y + g*t = 16.07 m/s + 9.8 m/s² * 3.75 s = 53.32 m/s

Here, g is the acceleration due to gravity, which is approximately 9.8 m/s².

Step 3: Determine the final velocity in the horizontal direction.

In the absence of air friction, the horizontal velocity (vfx) remains constant throughout the motion:

vfx = v0x = 19.15 m/s

Step 4: Determine the magnitude of the final velocity.

The final velocity (vf) is the vector sum of the final horizontal and vertical velocities. We can use the Pythagorean theorem to find its magnitude:

vf = sqrt(vfx² + vfy²) = sqrt((19.15 m/s)² + (53.32 m/s)²) = 57.07 m/s

So, the stone is moving at 57.07 m/s just before it hits the ground.