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 2.4 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?
H=D+h= 14.6+2.4 =17 m.
H=gt²/2
t=sqrt(2H/g) =sqrt(2•17/9.8)=1.86 s.
v(x) =1 m/s.
L=v(x) •t=1•1.86 = 1.86 m.
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 12.0 m, the bottom of the wheel is 2.00 m above the ground and its rim is moving at a speed of 1.00 m/s. How far from the base of the Ferris wheel will the teddy bear land?
To find out how far from the base of the Ferris wheel the teddy bear will land, we need to calculate the horizontal distance traveled by the teddy bear while falling.
Let's break down the problem and look at the given information:
- Diameter of the Ferris wheel: 14.6 m
- Distance from the ground to the bottom of the wheel: 2.4 m
- Speed of the rim of the wheel: 1.0 m/s
First, let's determine the circumference of the Ferris wheel. The circumference of a circle is given by the formula: C = πd, where C is the circumference and d is the diameter.
C = π × 14.6 m
C ≈ 45.92 m
Since the bottom of the wheel is 2.4 m above the ground, we can subtract this height from the total distance traveled by the teddy bear.
Total distance traveled by the teddy bear = C - 2.4 m
Total distance traveled by the teddy bear ≈ 45.92 m - 2.4 m
Total distance traveled by the teddy bear ≈ 43.52 m
Now, we can calculate the time it takes for the teddy bear to fall. Since we know that the rim of the Ferris wheel is moving at a speed of 1.0 m/s and the circumference of the wheel is 45.92 m, we can use the formula: time = distance ÷ speed.
Time taken for the teddy bear to fall = Total distance traveled by the teddy bear ÷ speed of the rim
Time taken for the teddy bear to fall ≈ 43.52 m ÷ 1.0 m/s
Time taken for the teddy bear to fall ≈ 43.52 s
Finally, we need to calculate the horizontal distance traveled by the teddy bear. Since the teddy bear falls straight down, this distance is equal to the speed of the rim multiplied by the time taken for the teddy bear to fall.
Horizontal distance traveled by the teddy bear = speed of the rim × time taken for the teddy bear to fall
Horizontal distance traveled by the teddy bear ≈ 1.0 m/s × 43.52 m
Horizontal distance traveled by the teddy bear ≈ 43.52 m
Therefore, the teddy bear will land approximately 43.52 meters horizontally from the base of the Ferris wheel.