in 1989 michel menin of france walked on a tightrope suspended under a balloon nearly at an altitude of 3150 m above the ground . suppose a coin falls from menin's pocket during his walk . how high above the ground is the coin when its speed is 60 m/s ?
To determine the height of the coin above the ground when its speed is 60 m/s, we need to use the principles of free fall and motion equations.
1. Initially, we assume that the coin falls vertically downward without any air resistance.
2. We can use the equation for free fall motion: h = u*t + (1/2) * g * t^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
3. Since the coin is falling vertically downwards, the initial velocity (u) is 0 m/s (as it does not have any initial upward velocity).
4. Rearranging the equation to isolate t, we get: t = √(2h/g).
5. Plug in the given values: h = 3150 m, g = 9.8 m/s^2.
6. Calculate the time taken for the coin to reach the ground: t = √(2 * 3150 / 9.8) ≈ 24.47 seconds.
7. Now, we can use the time to find the distance fallen by the coin using the equation s = u*t + (1/2) * g * t^2, where s is the distance traveled by the coin and u is still 0 m/s.
8. The distance the coin falls when its speed is 60 m/s is given by: s = 0 * 24.47 + (1/2) * 9.8 * (24.47)^2.
9. Calculate the distance: s ≈ 3006.615 m.
10. Finally, subtract the distance fallen by the coin from the initial height to find the height of the coin above the ground: 3150 m - 3006.615 m ≈ 143.385 meters.
So, when the coin's speed is 60 m/s, it is approximately 143.385 meters above the ground.
To find how high above the ground the coin is when its speed is 60 m/s, we can use the principles of projectile motion.
First, let's consider the horizontal motion of the coin. Since no horizontal force acts on the coin, its horizontal velocity remains constant. Therefore, the horizontal distance traveled by the coin is not relevant to finding its height above the ground.
Now, let's focus on the vertical motion of the coin. The only force acting on the coin vertically is gravity, which causes it to accelerate downward at a rate of approximately 9.8 m/s^2.
To determine the height of the coin when its speed is 60 m/s, we need to find the time it takes for the coin to reach that speed. We can use the equation of motion:
v = u + gt
where:
v = final velocity (60 m/s)
u = initial velocity (0 m/s, as the coin was initially at rest)
g = acceleration due to gravity (-9.8 m/s^2, negative because it acts downward)
t = time
Rearranging the equation, we get:
t = (v - u) / g
t = (60 m/s - 0 m/s) / -9.8 m/s^2
t ≈ -6.12 s
Since time cannot be negative in this context, we neglect the negative sign and consider only the magnitude of time, which is 6.12 s.
Next, we can use the equation of motion to determine the height of the coin from the ground:
s = ut + (1/2)gt^2
where:
s = height
u = initial velocity (0 m/s)
t = time (6.12 s)
g = acceleration due to gravity (-9.8 m/s^2)
Substituting the values into the equation, we have:
s = 0 + (1/2)(-9.8 m/s^2)(6.12 s)^2
s ≈ -179.8 m
Again, we neglect the negative sign and consider only the magnitude of the height.
Therefore, when the coin's speed is 60 m/s, it is approximately 179.8 meters above the ground.