Question

A ball is thrown at 22 m/s at 45 degrees to the horizontal. A 5 foot tall fence is located 100 meters away. Does
the ball make it over the fence?

Answer 1

Answer on Question #49182 – Physics – Mechanics | Kinematics | Dynamics

1. A ball is thrown at $22 \, \text{m/s}$ at 45 degrees to the horizontal. A 5 foot tall fence is located 100 meters away. Does the ball make it over the fence?

$$\left\{ \begin{array}{l} x = v_0 \cos \varphi \cdot t \\ y = v_0 \sin \varphi \cdot t - \frac{g t^2}{2} \end{array} \right.$$

The total time of a fly (without any obstacles) can be found from the equation $y = 0$:

$$v_0 \sin \varphi \cdot t - \frac{g t^2}{2} = 0, \quad t_1 = \frac{2 v_0 \sin \varphi}{g} = \frac{2 \cdot 22 \cdot \sin 45{}^\circ}{9.8} \approx 3.17 \, (\text{s}).$$

The total distance in $X$-direction will be $x(t_1) = v_0 \cos \varphi \cdot t_1 = 22 \cdot \cos 45{}^\circ \cdot 3.17 = 49.3 \, (\text{m})$.

$x(t_1) < l = 100 \, \text{m}$, so, the ball will drop before the fence.

Answer: the ball will not make the fence over.

http://www.AssignmentExpert.com/