Question

jason throws a ball horizontally off a 300 meter cliff at 15.0 m/s. how long will it travel before it hits the ground? use significant figures, and estimate g to be equal to 9.81 m/s². round the answer to the nearest hundredth. a 10 seconds b 6.78 seconds c 7.82 seconds d 8.72 seconds e 3.45 seconds

Explanation:

Step1: Analyze vertical - motion

The vertical - motion of the ball is a free - fall motion. The initial vertical velocity $v_{0y}=0$ m/s, the acceleration due to gravity $g = 9.81$ m/s², and the vertical displacement $y=- 300$ m (taking downwards as negative). The equation for vertical displacement is $y = v_{0y}t+\frac{1}{2}at^{2}$. Since $v_{0y} = 0$ m/s, the equation simplifies to $y=\frac{1}{2}(-g)t^{2}$.

Step2: Solve for time $t$

We have $y=\frac{-1}{2}gt^{2}$, so $t=\sqrt{\frac{-2y}{g}}$. Substitute $y = - 300$ m and $g = 9.81$ m/s² into the formula: $t=\sqrt{\frac{-2\times(-300)}{9.81}}=\sqrt{\frac{600}{9.81}}\approx\sqrt{61.1621}\approx7.82$ s.

Answer:

C. 7.82 seconds