Question

Calculate the height of a cliff if it takes 2.35 s for a rock to hit the ground when thrown straight up from the cliff with an initial velocity of 8.00 m/s.

a) 22.1 m
b) 27.3 m
c) 32.5 m
d) 37.7 m

Answer 1

The height of the cliff is approximately 27.3 m. Thus, the correct answer is option b 27.3 m.

Step-by-step explanation:

When an object is thrown upwards, its motion can be analyzed using the equations of motion. In this case, the rock is thrown straight up from the cliff with an initial velocity of 8.00 m/s, and it takes 2.35 seconds to hit the ground.

We can use the following kinematic equation to determine the height (h) of the cliff:

`\[ h = v_0t - (1)/(2)gt^2 \]`

Where:

-
`\( v_0 \)` is the initial velocity,

- t is the time of flight,

- g is the acceleration due to gravity (approximately 9.8 m/s²).

Substituting the given values:

`\[ h = (8.00 \, \text{m/s})(2.35 \, \text{s}) - (1)/(2)(9.8 \, \text{m/s}^2)(2.35 \, \text{s})^2 \]`

Calculating this expression yields the height of the cliff. Solving for h gives h ≈ 27.3 m.

Therefore, the height of the cliff from which the rock was thrown is approximately 27.3 meters. This result is obtained by considering the initial velocity, time of flight, and the effects of gravity on the projectile's motion. Therefore, the correct answer is option b 27.3 m.