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

Answer:

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:

$v = \omega R = 70\times 0.46 = 32.2\ m/s$

Total time taken:

$t = \frac{2vsin\theta}{g} = \frac{2\times 32.2sin45^{\circ}}{9.8} = 4.646\ s$

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

$x = vt + \frac{1}{2}at^{2} = 32.2cos45^{\circ}\times 4.646 = 105.78\ m$

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.