Question

A golf ball is thrown horizontally off a cliff at a velocity of 20 meters per second and takes 4 seconds to reach the ground below. Calculate the impact velocity of the ball

Answer 1

First, we need to calculate the vertical component of the ball's velocity at impact. To do this, we can use the formula:

v = u + at

Where:
v = final velocity (m/s)
u = initial velocity (m/s)
a = acceleration (m/s^2)
t = time (s)

Since the ball is in free fall, the acceleration due to gravity is -9.8 m/s^2 (negative because it is acting downward). The initial vertical velocity of the ball is 0 m/s, as it is thrown horizontally. The time the ball takes to reach the ground is 4 seconds.

Plugging these values into the formula, we get:
v = 0 + (-9.8 * 4)
v = -39.2 m/s

So, the vertical component of the impact velocity is -39.2 m/s.

Next, we can calculate the horizontal component of the impact velocity. Since there is no horizontal acceleration, the horizontal component of the velocity remains constant at 20 m/s.

To find the total impact velocity, we can use the Pythagorean theorem:

v = sqrt((vertical velocity)^2 + (horizontal velocity)^2)
v = sqrt((-39.2)^2 + (20)^2)
v = sqrt(1534.24 + 400)
v = sqrt(1934.24)
v ≈ 44 m/s

Therefore, the impact velocity of the golf ball is approximately 44 meters per second.