A cannonball is shot (from ground level) with an initial horizontal velocity of 33.0 m/s and an initial vertical velocity of 25.0 m/s.
What is the initial speed of the cannonball?
To find the initial speed of the cannonball, we need to use the concept of vector addition. The initial horizontal and vertical velocities of the cannonball can be combined using the Pythagorean theorem.
The Pythagorean theorem states that in 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.
In this case, the initial horizontal velocity (33.0 m/s) and the initial vertical velocity (25.0 m/s) are the two sides of the triangle, and the initial speed we are trying to find is the hypotenuse.
Using the Pythagorean theorem equation:
initial speed^2 = (initial horizontal velocity)^2 + (initial vertical velocity)^2
Plugging in the values:
initial speed^2 = (33.0 m/s)^2 + (25.0 m/s)^2
Simplifying:
initial speed^2 = 1089 m^2/s^2 + 625 m^2/s^2
initial speed^2 = 1714 m^2/s^2
To get the initial speed, we need to take the square root of both sides of the equation:
initial speed = √(1714 m^2/s^2)
Using a calculator, we find that the initial speed of the cannonball is approximately 41.40 m/s.
To find the initial speed of the cannonball, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the horizontal velocity and the vertical velocity of the cannonball form the legs of the right-angled triangle, and the initial speed of the cannonball is the hypotenuse.
Using the Pythagorean theorem, we have:
initial speed^2 = (horizontal velocity)^2 + (vertical velocity)^2
initial speed^2 = (33.0 m/s)^2 + (25.0 m/s)^2
initial speed^2 = 1089 m^2/s^2 + 625 m^2/s^2
initial speed^2 = 1714 m^2/s^2
Taking the square root of both sides, we find:
initial speed = √(1714 m^2/s^2)
initial speed ≈ 41.4 m/s
Therefore, the initial speed of the cannonball is approximately 41.4 m/s.