Question

a batsman hits a ball at 45 degree angle with horizontal and with a velocity of 20 m/s.the ball started to going over the bowler. a fielder from the mid-field ran to catch it. but the fielder could not reach in time . that's why the ball crosses the boundary line and it became a 6 run for the batsman.the ball travels 35 m at field. if the fielder is able to take catch at a height of 3 m , and if the fielder could reach in time to the boundary line, would he be able to catch the ball?

Answer 1

Answer on Question #52426, Physics, Mechanics | Kinematics | Dynamics

A batsman hits a ball at 45 degree angle with horizontal and with a velocity of $20\,\mathrm{m/s}$. The ball started to going over the bowler. A fielder from the mid-field ran to catch it. But the fielder could not reach in time. That's why the ball crosses the boundary line and it became a 6 run for the batsman. The ball travels $35\,\mathrm{m}$ at field. If the fielder is able to take catch at a height of $3\,\mathrm{m}$, and if the fielder could reach in time to the boundary line, would he be able to catch the ball?

Solution:

Given:

$$\begin{array}{l} x_1 = 35\,\mathrm{m}, \\ \theta = 45{}^\circ, \\ v_0 = 20\,\mathrm{m/s}, \\ h = ? \\ \end{array}$$

Neglecting air resistance, the projectile is subject to a constant acceleration $g = 9.81\,\mathrm{m/s^2}$, due to gravity, which is directed vertically downwards.

Equations related to trajectory motion (projectile motion) are given by

Horizontal distance, $x = v_{0x}t$

Vertical distance, $y = v_{0y}t - \frac{1}{2}gt^2$

where $v_0$ is the initial velocity.

We have

$$x_1 = 35\,\mathrm{m}$$

Thus, the time of ball's flight to the boundary line

$$t = \frac{x_1}{v_{0x}} = \frac{x_1}{v_0 \cos \theta} = \frac{35}{20 \cdot \cos 45{}^\circ} = 2.475\,\mathrm{s}$$

Vertical distance,

$$h = y = v_0 \sin \theta t - \frac{1}{2}gt^2 = 20 \cdot \sin 45{}^\circ \cdot 2.475 - \frac{9.8 \cdot 2.475^2}{2} = 4.986\,\mathrm{m}$$

Hence, at the boundary line ball will be at $\approx 5\,\mathrm{m}$ height.

Answer: The fielder would not be able to catch the ball.

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