a stone is thrown horizontally at a speed of 5.o m/s from the top of a cliff 78.4 m high. How long does it take the stone to reach the bottom of the cliff?

Question

a stone is thrown horizontally at a speed of 5.o m/s from the top of a cliff 78.4 m high. How long does it take the stone to reach the bottom of the cliff?

Answer 1

distance = 1/2gt^2. You know distance and g, solve for time. It doesn't matter what the horizontal speed is as the stone will fall at the same rate as if it were dropped. True, the stone won't land at the foot of the cliff but further away from the cliff.

Answer 2

To find the time it takes for the stone to reach the bottom of the cliff, we can use the equation of motion:

distance = initial velocity × time + 0.5 × acceleration × time²

Since the stone is thrown horizontally, the initial vertical velocity is zero. Therefore, the equation simplifies to:

distance = 0.5 × acceleration × time²

The acceleration in this case is due to gravity and is equal to 9.8 m/s² (assuming no air resistance).

Given that the cliff height is 78.4 m, we can substitute the values into the equation:

78.4 = 0.5 × 9.8 × time²

To solve for time, we rearrange the equation:

time² = (78.4 / (0.5 × 9.8))

time² = (78.4 / 4.9)

time² = 16

Taking the square root of both sides, we find:

time = √16

time = 4 seconds

Therefore, it takes the stone 4 seconds to reach the bottom of the cliff.

Answer 3

To find the time it takes for the stone to reach the bottom of the cliff, we can use the kinematic equation:

𝑑 = 𝑣0 × 𝑡 + (1/2) × 𝑎 × 𝑡^2

Where:
- 𝑑 is the vertical distance traveled (78.4 m),
- 𝑣0 is the initial velocity in the vertical direction (0 m/s because the stone is thrown horizontally),
- 𝑡 is the time taken, and
- 𝑎 is the acceleration due to gravity (-9.8 m/s^2).

Since the stone is thrown horizontally, the initial vertical velocity (𝑣0) is 0 m/s. Thus, the kinematic equation simplifies to:

78.4 = (1/2) × (-9.8) × 𝑡^2

Simplifying further:

78.4 = -4.9 𝑡^2

Now, rearrange the equation to solve for 𝑡^2:

𝑡^2 = 78.4 / -4.9

𝑡^2 = -16

Now, we can discard the negative value since time can't be negative in this context. So, we take the positive square root:

𝑡 = √16

𝑡 = 4 seconds

Therefore, it takes 4 seconds for the stone to reach the bottom of the cliff.

a stone is thrown horizontally at a speed of 5.o m/s from the top of a cliff 78.4 m high. How long does it take the stone to reach the bottom of the cliff?

distance = 1/2*g*t^2. You know distance and g, solve for time. It doesn't matter what the horizontal speed is as the stone will fall at the same rate as if it were dropped. True, the stone won't land at the foot of the cliff but further away from the cliff.

To find the time it takes for the stone to reach the bottom of the cliff, we can use the equation of motion:

To find the time it takes for the stone to reach the bottom of the cliff, we can use the kinematic equation:

distance = 1/2gt^2. You know distance and g, solve for time. It doesn't matter what the horizontal speed is as the stone will fall at the same rate as if it were dropped. True, the stone won't land at the foot of the cliff but further away from the cliff.