A car travelling along picks up a nail. The nail gains a maximum height 66 cm above the ground in .075 seconds. Determine the followings.
a) angular velocity of the wheel in radians per second.
b) the distance travelled by the car in 2.5 seconds.
A car traveling on a road picks up a nail lying on the ground. For this to happen, the nail that was lying on the ground gets stuck to the tire of the car when it passes over it. The nail gains a maximum height of 66 cm in 0.75 s. This gain in height is equal to the diameter of the car's wheel. (It is assumed you meant 66 cm not 66 m.) This gives the radius of the car's tire as 33 cm.
As the nail reaches its maximum height in 0.075 s, the wheel of the car has rotated by one radian in 0.075 s. The angular velocity of the car is equal to 1/0.075 = 13.33 radians/second
The radius of the car is 33 cm, to convert angular velocity to linear velocity multiply the angular velocity by the radius. The linear velocity is 13.33*33 cm/s. In 2.5 s the car travels 1099.7 cm
The angular velocity of the car is 13.33 radians/second and it travels 1099.7 cm in 2.5 s.