A ball is thrown horizontally from a height of 20 m andhits the ground with a speed that is three times its initial speed.What is the initial speed?

To solve this problem, we need to use the equations of motion.

Step 1: Identify the given information The height (h) from which the ball is thrown is 20 m. The final speed (v) is three times the initial speed (u).

Step 2: Use the equation of motion We can use the second equation of motion, which is v^2 = u^2 + 2gh, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Step 3: Substitute the given values into the equation Since the final speed is three times the initial speed, we can substitute v with 3u. The equation becomes (3u)^2 = u^2 + 29.820.

Step 4: Simplify the equation 9u^2 = u^2 + 392 8u^2 = 392 u^2 = 49 u = sqrt(49)

Step 5: Solve for u u = 7 m/s

So, the initial speed of the ball is 7 m/s.