Question

A weighted ball is thrown upward. Its initial vertical component of

velocity is 30 m/s and its initial horizontal component of velocity is 10
m/s. What is the ball's speed 4 s later? Use g = 10 m/s^2. You will need a
sketch to solve. *

Answer 1

The ball's speed 4 seconds later is 10√2 m/s.

Step-by-step explanation:

To find the ball's speed 4 seconds later, we can use the given initial vertical and horizontal components of velocity. Since the only force acting on the ball is gravity, the vertical component of velocity decreases at a rate of 10 m/s².

At t = 4 seconds, the vertical component of velocity will be:

Vertical velocity = initial vertical velocity - (acceleration due to gravity * time)

Vertical velocity = 30 m/s - (10 m/s² * 4 s)

= 30 m/s - 40 m/s

= -10 m/s

The negative sign indicates that the velocity is directed downward.

To find the total speed, we can use the Pythagorean theorem:

Speed = √(horizontal velocity² + vertical velocity²)

Speed = √((10 m/s)² + (-10 m/s)²) = √(100 m²/s² + 100 m²/s²)

= √200 m²/s²

= √(2 * 100) m/s

= 10√2 m/s