Question

⦁ A baseball is struck by a bat 46 cm from the axis of rotation when the angular velocity of the bat is 70 rad/s. If the ball is hit at a height of 1.2 m at an angle of 45 degrees, will the ball clear a 1.2 m fence 110 m away (assume the initial velocity of the ball is the same as the linear velocity of the bat at the point at which it is struck?

Answer 1

No, the ball will not clear the fence.

Solution:

Angular velocity,
`\omega = 70\ rad/s`

Height, h = 1.2 m

Angle,
`\theta = 45^(\circ)`

Distance covered by the ball, d = 110 m

Length of the fence, l = 1.2 m

Radius of the axis, R = 46 cm = 0.46 m

Now,

To calculate the linear velocity of the ball, v:

`v = \omega R = 70* 0.46 = 32.2\ m/s`

Total time taken:

`t = (2vsin\theta)/(g) = (2* 32.2sin45^(\circ))/(9.8) = 4.646\ s`

The distance at which the ball falls, with a = 0 is given by:

`x = vt + (1)/(2)at^(2) = 32.2cos45^(\circ)* 4.646 = 105.78\ m`

Since, the ball has to clear a fence 1.2 m long and a t a distance 110 m away, clearly it will not be able to cross it.