At a county fair, a boy takes his teddy bear on the giant Ferris wheel. Unfortunately, at the top of the ride, he accidentally drops his stuffed buddy. The wheel has a diameter of 14.6 m, the bottom of the wheel is 1.1 m above the ground and its rim is moving at a speed of 1.0 m/s. How far from the base of the Ferris wheel will the teddy bear land?
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The speed of a point of the rim of a car is 20m/s the diameter is 50cm what is the angular velocity of the wheel
To find the distance from the base of the Ferris wheel where the teddy bear will land, we need to first calculate the time it takes for the teddy bear to fall from the top to the ground, and then determine the horizontal distance it travels during that time.
Let's break down the problem step by step:
Step 1: Calculate the time of fall
To determine the time it takes for the teddy bear to fall from the top of the Ferris wheel to the ground, we can use the equation for free fall:
h = (1/2) * g * t^2
Where h is the height (1.1 m in this case), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time of fall.
Rearranging the equation to solve for t, we get:
t^2 = (2 * h) / g
t = sqrt((2 * h) / g).
Plugging in the values, we have:
t = sqrt((2 * 1.1 m) / 9.8 m/s^2)
t ≈ sqrt(0.224 m) ≈ 0.474 s.
Step 2: Calculate the horizontal distance
Now that we know the time it takes for the teddy bear to fall, we can find the horizontal distance it travels during that time. We can use the formula for distance (d) as speed (v) multiplied by time (t):
d = v * t.
In this case, the speed (v) is given as 1.0 m/s, and the time (t) is approximately 0.474 s:
d = 1.0 m/s * 0.474 s
d ≈ 0.474 m.
Therefore, the teddy bear will land approximately 0.474 meters from the base of the Ferris wheel.