Question

A ball is thrown horizontally with an initial speed of 10 m S ^ - 1 from an 80 m cliff. How long does it take to reach the ground?

Answer 1

To determine the time it takes for the ball to reach the ground when thrown horizontally from an 80 m cliff with an initial speed of 10 m/s, we can use the kinematic equation for vertical motion:

$d=\frac{1}{2}g{t}^2$

where:

• d is the vertical distance traveled (80 m in this case),
• g is the acceleration due to gravity (approximately 9.8 m/s^2),
• t is the time.

In this scenario, the initial vertical velocity (v₀) is 0 because the ball is thrown horizontally. Since the initial vertical velocity is zero, the equation simplifies to:

$d=\frac{1}{2}g{t}^2$

Rearranging the equation to solve for time (t), we get:

$t=\sqrt{\frac{2d}{g}}$

Substituting the given values, we have:

$t=\sqrt{\frac{2\cdot 80}{9.8}}$

Solving this equation, we find:

t≈4.04 secondst approx 4.04 ext{ seconds}t≈4.04 seconds</span