Final answer:
To find the ball's final speed after being thrown from a height and landing 2 seconds later, the equation of motion v = u + at is used, with gravity as the acceleration. Assuming no initial throw velocity, the final speed is calculated to be 19.62 m/s.
Step-by-step explanation:
To find the final speed of a ball thrown down from a height of 30m and lands 2 seconds later, we need to use the equations of motion for uniformly accelerated motion, specifically, the one that relates velocity, acceleration, and time. Assuming the only acceleration acting on the ball is due to gravity (which is 9.81 m/s²), and disregarding air resistance, the equation to use is:
v = u + at
Where v is the final velocity, u is the initial velocity (which is zero if the ball is simply dropped, but could be more if it was thrown down), a is the acceleration due to gravity, and t is the time taken. As the problem does not state that there was an initial velocity when the ball was thrown down, we can assume it to be zero. Thus, the final speed v can be calculated as:
v = 0 + (9.81 m/s² * 2 s)
The calculation gives us v = 19.62 m/s. This is the ball's final speed when it lands.