Question

A ball is kicked at ground level with an initial velocity of 18 m/s in the horizontal direction and 14 m/s in the vertical direction. What is the total initial velocity of the ball?

1) 20 m/s
2) 22 m/s
3) 24 m/s
4) 26 m/s

Answer 1

Using the Pythagorean theorem, the total initial velocity of a ball kicked with horizontal and vertical components of 18 m/s and 14 m/s, respectively, is found to be approximately 23 m/s, which does not match the options provided.

Step-by-step explanation:

To calculate the total initial velocity of the ball, which has components of 18 m/s in the horizontal direction and 14 m/s in the vertical direction, we use the Pythagorean theorem. This theorem states that for a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Here, our hypotenuse is the resultant initial velocity, and the two other sides are the horizontal and vertical velocity components of the ball.

Step-by-step calculation:

1. Write down the equation derived from the Pythagorean theorem: V_total^2 = V_horizontal^2 + V_vertical^2
2. Insert the values for V_horizontal and V_vertical: V_total^2 = 18^2 + 14^2
3. Calculate the squares: V_total^2 = 324 + 196
4. Add the squares: V_total^2 = 520
5. Take the square root of the sum to find the total initial velocity: V_total = √520
6. Calculate the square root: V_total ≈ 22.8 m/s
7. Round to the nearest whole number, if needed: V_total ≈ 23 m/s

Therefore, none of the options provided (20 m/s, 22 m/s, 24 m/s, and 26 m/s) are correct. The total initial velocity of the ball is approximately 23 m/s.