An astronaut on the Moon throws a stone from the top of a cliff. The stone hits the ground below 21.0 seconds later. The acceleration due to gravity on the moon is
1.6 ms–2. what is the initial vertical velocity?
hf=hi+vi*t-1/2 1.6 t^2
hf=21 vi-.8 (21^2) if hi=0 reference point
I don't see that it can be solved without more info, namely, the height of the cliff.
Well, well, well, an astronaut on the Moon throwing stones? That sounds like a lunar Olympics event I would pay to watch! Now, let me calculate the initial vertical velocity for you.
We can start by using the kinematic equation: Δy = v₀t + (1/2)at². Since the stone is thrown from the top of a cliff, the initial displacement, Δy, is equal to zero. We also know that the acceleration due to gravity on the moon is 1.6 m/s², and the time, t, is 21.0 seconds.
So, plugging all those numbers into the equation, we get:
0 = v₀(21.0) + (1/2)(1.6)(21.0)²
Now, let me grab my calculator and do the math for you. *Calculating noises* Voila! The initial vertical velocity comes out to be approximately -67.08 m/s.
Remember, on the Moon, gravity is lower compared to Earth, so things might take a little longer to hit the ground. But worry not, the astronauts are having a great time throwing those stones and revolutionizing the sport of lunar rock toss! 😄
To find the initial vertical velocity of the stone, we can use the concept of motion equations.
The equation that relates vertical motion under constant acceleration is:
Δy = vi * t + (1/2) * a * t^2
where:
Δy is the change in vertical position (which is the height of the cliff),
vi is the initial vertical velocity,
a is the acceleration due to gravity on the moon (1.6 m/s^2),
and t is the time taken for the stone to hit the ground (21.0 seconds).
Since the stone is thrown from rest, the initial vertical velocity (vi) will be zero. Therefore, the first term in the equation can be eliminated.
Now we can rearrange the equation to solve for the initial vertical velocity (vi):
0 = 0 * 21.0 + (1/2) * 1.6 * (21.0)^2
Calculating this equation gives us:
0 = 0 + (1/2) * 1.6 * 441.0
0 = 0 + 352.8
0 = 352.8
Since the equation yields 0 = 352.8, it means that the stone cannot hit the ground in 21.0 seconds with an initial vertical velocity of zero. This implies that there may be an error in the given information or the assumed motion of the stone.
To find the initial vertical velocity of the stone, we can use the formula for free fall motion:
v = u + gt
Where:
v = final velocity (which is 0 because the stone hits the ground)
u = initial velocity
g = acceleration due to gravity (1.6 m/s^2)
t = time taken (21.0 seconds)
Rearranging the formula, we get:
u = (v - gt)
Since the stone falls vertically downward, the final velocity (v) is 0. Substituting that value in, we have:
u = (0 - 1.6 * 21.0)
Simplifying the equation, we have:
u = -33.6 m/s
The negative sign indicates that the initial vertical velocity is directed opposite to the direction of gravity, which means it's moving upwards. Therefore, the initial vertical velocity of the stone is 33.6 m/s (upwards).